Conceptual Design of an "Inexpensive" Single-Seat Motorglider

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  1. Oct 20, 2014 #21

    Topaz

    Topaz

    Topaz

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    Other Requirements, Specifications, and Restrictions

    Handling Qualities
    I am a low-time pilot. As such, I want to make sure that the airplane isn't more than I can handle. I've already made sure the stall speed is low. When I need values for things like tail volumes, etc., and other specifications that define stability and handling qualities, I'll use values from trainers and basic aircraft such as the C-152, PA-38, and C-172. In any event, measurable handling characteristics should always meet or exceed CS-22 minimums.

    Trailerability
    This has been a tough question to answer in any kind of rational way. Hangars are insanely expensive to rent in southern California. You could rent an apartment for less in many cases. Tie-down rentals are very high and their price constantly fluctuates with demand, making any analysis obsolete almost as soon as it's completed. I'd certainly like to save the monthly expense of a hangar or tie-down. On the other hand, making the aircraft trailerable adds weight and cost to a design where weight and cost are already going to be at a premium.

    After vacillating back and forth over this for a couple of days, and re-reading the various related threads on HBA, I've decided to simply punt the final decision down the road into the design phase. I'll set trailerability as a goal, but it's not a threshold requirement. If everything else about the airplane meets my requirements but making it trailerable pushes it out of the cost threshold, I'll allow that requirement to fail and do the airplane without the ability to regularly trailer it. I'll just have to figure out where and how to store it affordably at that time. This means "trailerability" becomes another trade-study for the program. The storage space for the airplane would be my garage, shown in Figure 1 below.

    Requirements related to Trailerability
    If the aircraft ends up being trailerable, it imposes a few requirements on the project:
    .
    Maximum Legal Road Width - California
    8 feet​
    Maximum Legal Road Length - California
    40 feet​
    Trailer Required - California
    The aircraft may not be trailered on its own landing gear.​
    Garage Door Opening Width (Physical Limitation)
    8 feet​
    Maximum one-person assembly or disassembly time

    Fifteen Minutes​
    .
    Build Space Restrictions
    My baseline build-space is my one-car garage. The rules of my condominium association require that the garage be used to park a car at all times, and are enforced by a parking permit system. Temporary parking passes can be obtained for short-term outside storage or for visitors. So my build will need to share the garage with one vehicle most of the time. The smaller of my two vehicles is my '73 Porsche 914, which I want to store indoors anyway (they tend to rust). The layout of the garage is shown in Figure 1 below. There is a non-removable shelf at the back of the garage, and a structural beam crossing the ceiling. The automatic garage door opener has been removed since I prepared this drawing several years ago.

    Storage Space.jpg
    Figure 1 - My Garage
    The green area denotes wing storage, blue for fuselage. These can be reversed if need be.
    My preference is to store the fuselage high in the blue volume, allowing space for my work table below.
    If the wing chord is short enough, it may be better to store the wings over the work table instead.

    Pulling out my tape measure, I get the following workspace dimensions:
    .
    Maximum Part Length (These values include clearances - actual garage maximum dimensions are approximately 1' longer)
    19 feet maximum (object extends under or over the back shelf)
    17 feet easy and practical work and storage (front edge of the shelf to the door)​
    .
    Regular Work Table Size
    The work table will run along the left wall of the garage, looking in. The garage door spring occupies about the first foot of the available length.
    Length: 16 feet long
    Width: 3 feet wide​
    .
    Tool Noise
    I have an unusual restriction for my build. My garage is underneath an occupied condominium unit - and it's not my own. The ceiling of my garage is the floor of their unit. Also, there are other units directly across the garage access road from my garage, approximately 25 feet away. My complex has specific rules against the use of power tools in the garage spaces, not to mention that I like my neighbors and don't want to annoy them with a lot of noise. Unhappy neighbors leads to complaints to the Association, which ultimately leads to my build effectively being shut down. Yes, the Association has the power to do that. There are no rental shops available in the area, and driving any significant distance means I won't be out building as often.

    All that said, I have no intention of strictly adhering to the rules on this subject. You can't build an airplane effectively without any power tools at all. You could do it, but going all 18th century would needlessly extend the build. Fortunately, I have some options:
    .
    • I work for myself, so I have some flexibility to adjust my work hours when my workload permits. Unless I need to work with freelancers, have a particularly large project on tight deadline, a client meeting, or need to devote time to date-driven marketing, sales, or admin tasks for my own business, I can often go in to work early and then close the shop early, giving me a couple of hours a day for the build before my neighbors come home from work. On hot summer days, I can sometimes take those couple of hours in the morning after they've gone to work.
    • Depending upon the materials I choose for the build, I can also work in the evenings. I just need to control the noise I produce, mostly as a consequence of the tools the material requires. There will be some pieces that are just going to be noisy to build but, to an extent, I can also schedule "noisy" work for the daytime work sessions, and "quiet" work for evening or weekend sessions.
    • I'm making the acquaintance of my neighbors,and especially the ones that will be most affected by my build noise. I've done some small projects in my garage using the same time patterns I intend to use for the airplane, and asked those neighbors if I was making too much noise. So far, everyone has been very gracious and said that it hasn't been a problem. They've noted the noise occasionally, but so long as it's not more frequent or louder, they've said they have no complaint. Mostly they just seemed happy that I asked. I've stressed that if my shop work ever does become annoying, to please let me know directly as soon as possible and that I'd do what I could to make it right for them. Much better to have them complain to me than the Association! I think it's really important to be kind to your neighbors in a project like this.
    .
    To a certain extent then, choosing a construction material that requires less use of power tools, and designing the airplane to minimize the need, gives me more opportunities to work on the airplane on evenings or weekends. This gives me more available working hours during a given week without risking a complaint to the association about noise. That's a big plus. So I'm going to add this subjective goal for the project: The airplane should require a minimum of noisy power tools for its construction.

    Technology Availability
    In Aircraft Design: A Conceptual Approach, Dan Raymer talks quite a bit about looking at the level of technology that will be introduced into the aircraft design, particularly where it concerns technologies that will need to be developed for the design. While this usually isn’t much of a concern for homebuilt designs, it does come up sometimes. When Rutan decided to adapt the German akaflieg’s foam-and-glass technology to then-modern American homebuilding, that was a technological risk in terms of having to develop that technology for the purpose he had in mind.

    For this airplane, I want to minimize the amount of technology development I’ll need to perform. There are four areas where I am willing to explore adapting or developing new technology for this aircraft. In all other ways, I’ll use existing technologies that have already been demonstrated in other aircraft.
    .
    Engines: If it should prove possible to develop this airplane for the crop of industrial motors with which people have been tinkering for airplane application, I’m willing to explore that provided it can be shown to result in a significant cost savings for this one-off aircraft. Using a dedicated aircraft engine (certified or experimental) may result in savings compared to adapting an industrial motor, or the reverse may be true. This will be a design study for the project.
    .
    Throttle and Air Brake Controls: I would very much like to try out my combined throttle/drag-brake “quadrant” control system on this airplane.
    .
    Landing Gear Retraction: I have an idea for a low-cost and simple landing gear retraction system that may be applicable here. I’d like to try that out if possible.
    .
    Commercial tablet-based flight display: This may end up being a commercial system that I purchase outright, if one can be found for a reasonable price. Otherwise, I would like to experiment with a low-cost primary flight display hosted on a commercial Android OS tablet. This does not have to be installed in the airplane for first flight, but rather can be a developmental item for after the aircraft is done with its flight-test period. ​
    .
    Safety and Crashworthiness
    Airplanes crash. That’s reality. People are injured and sometimes die as a result. To ignore that fact is foolish. I’ve lost two friends to airplane crashes. To become obsessed with it results in an airplane that’s very likely to be heavily compromised in every other area. I’m going to say two things about safety:
    .
    1. I’m also not up to re-inventing the wheel when it comes to developing safety standards that are a reasonable balance between safety and inflicting too much of a performance penalty on the aircraft. Wherever practical, the airplane will try to satisfy the safety requirements in CS-22 for single-seat powered sailplanes.
    2. SVSUSteve, wherever you are, you had an effect on me. And watching my friend Bill crash in front of me and sustain injuries that killed him later that day had an effect on me. Losing Woody just a few weeks later to another crash had an effect on me. Regardless of the overall method of construction, I would like this aircraft to have a welded steel-tube safety cage, unless I can be sure of meeting the CS-22 standards without one. The cage can be part of the primary structure, if need be to save weight.

    Total Project Cost
    I've made the choice that this will be an "inexpensive" airplane. What does that mean? I've pointed out before that it's impossible to state what "inexpensive" means without saying what kind of airplane will be built. In this case, I'm defining the airplane very tightly with this set of specifications and requirements. What's "inexpensive" in this context? And what's "inexpensive" to me in this context, given that this is a one-off airplane for my own use?

    It's really easy to overthink this. I could run all sorts of financial analyses, but I already know how much money I'd be willing to spend upon this airplane before it just makes more sense to shelve this project and focus upon the two-seater. I know, roughly, how much that latter airplane will cost and if this one costs more than a substantially large fraction of one that can carry two people, there's little point to me in "settling" for just one seat and substantially less cross-country capability. I'm also not taking market considerations into account here at all, since this airplane is just for me. If I develop a "production" version later, I'll worry about the business plan and economic viability of the airplane as a product at that time.

    What does deserve some consideration is what's included in the prices I'm about to set. Do I only include the airplane itself; just everything that leaves the ground? The airplane plus the trailer, since a trailerable aircraft isn't much good without a trailer? All of this plus the tools needed to build the airplane?

    Here's my thinking: Pretty much every tool I might buy to build this airplane is good for other purposes, be it building another airplane or another project of some kind. The tools aren't single use. I also already own quite a few of them. That money is already spent. So I'm not going to include them in the total. Same goes for work tables and suchlike.

    I am going to include the cost of the trailer, however. Since I've decided that this will be a trailerable airplane, a trailer is necessary to its use. It'll be important for me to make sure the trailer is as inexpensive as possible while being adequate to the task, since every dollar is taken from what's available to build the airplane itself.

    Another issue is that of new versus "scrounged" parts. Scrounging or buying "used" can result in very significant savings, of course. But it's not reliable. You can't depend upon the parts being available when you need them with any reasonable level of assurance. So my price estimates resulting from this study will reflect all parts and materials being purchased from regular retailers. Things like remanufactured instruments, such as those sold by Aircraft Spruce, are fine, since they're coming through a national retailer who stocks them as regular inventory. If I do decide to build this airplane, of course I'll try to find deals on some parts, but for planning purposes I'm going to assume that I have to buy everything retail.

    So after a little soul-searching and without further to-do, here are my threshold and goal project costs for the airplane and trailer together. Costs of tools is not included.

    Goal: $5,000

    Threshold: $8,500

    Yes, those are challenging numbers, and cost of building an airplane is one of the most controversial subjects ever discussed on HBA. Before anyone jumps in on how "realistic" these values might be, I'll remind you that determining whether or not the airplane I've defined in these specifications can be built for these kind of prices is the entire point of this design study. I'm not much interested in opinions about whether or not it can be done - I'm going to find out. If you think that building this airplane and a trailer for it is impossible for these prices, you may well be right! Or you're not. We'll find out at the end, and I personally think it's entirely worth my own time to go through this study to find the answer.

    So, now, after all of these posts above, I think I'm done defining the specifications and requirements for this design. I'm going to spend a couple of days reviewing my work and making sure that there's nothing else I need to pin down. I'm open to suggestions if someone can see that I've missed something important. Once I think I'm done here, I'll post a final requirements and specifications document.

    And then the actual design process begins.
     
    Last edited: Oct 20, 2014
  2. Oct 24, 2014 #22

    Topaz

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    Final Tweaks to Specifications and Requirements

    As I mentioned last time, I spent a couple of days reviewing my specifications and requirements document. I found three unaddressed items, but otherwise I'm pretty satisfied with what I have. I like what this airplane will be able to do, and at least at first blush it looks like it could be something that's done within my price limits.

    The three unaddressed items are:

    1) Goal baggage weight: I have a threshold requirement for this, but never set a goal requirement. I did stuff my target day-pack with a water bottle, lunch, jacket, and a change of shirts, and the weight wasn't anywhere near the 20 lbs. I have as a threshold, so I don't need to stretch this much for a goal. Jan Roskam's Aircraft Design Part 1 suggests 30 lbs. as a target baggage weight for "short to medium trips", and my range goal certainly falls in the "short" category. So 30 lbs. becomes my baggage weight goal.

    It would be nice if the airplane would take full baggage, full fuel, and full pilot, so I'll stipulate that for my goal baggage weight. I already have a trade study listed for payload (pilot + baggage) versus airplane cost, so how much baggage I can really afford to carry will come out of that study, and whether or not I'll need to trade baggage weight for some of that larger pilot weight.

    2) Threshold Range Requirement: I'd set up my goal range requirement (Skylark Field [CA89] to Fresno Chandler [KFCH]), but while I alluded to a threshold requirement, I never plugged it into my requirements table. I'd like to be able to at least do Skylark Field to Oceano (L52) without having to stop to refuel. That's 223 nm plus the same 50 nm "reserve", for a total of 273 nm (314 sm). I have a trade study of range versus cost, but the difference between my goal and threshold range values is so small that I doubt it'll have a significant effect. We'll see.

    3) Goal Limit Load Requirement: I had settled on meeting CS 22.337 for the Utility category called out in that regulation as my threshold requirement. My use cases for this airplane (see "What" above) don't include aerobatics, so there really is no point in exceeding the threshold requirement. I'm going to say that there isn't any "goal" requirement for this value.

    And that is that. I'm comfortable and happy with all of these specifications, and it's time to close out this part of the process and move into the actual design phase. Here's the final draft of the requirements and specifications document for this airplane:

    View attachment DS54 - Requirements and Specifications FINAL.pdf

    Next Post: Starting in on the actual design process.
     
    Last edited: Nov 12, 2014
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  3. Oct 29, 2014 #23

    Topaz

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    Getting Started

    When I first started fiddling with airplane design, I did what everybody does, I suppose: I drew an airplane and tried to figure out how heavy it would be, what its stall speed would be, and so on. If it didn't meet the requirements I'd written up, I'd change things to try and make it work. Stall speed too high? Add more wing or bigger/better flaps. Range not enough? Bigger fuel tank.

    What I discovered is that this process turns into the engineering equivalent of "Whack-A-Mole". Make the fuel tank bigger and now the airplane is heavier, too, and it probably won't make the stall or climb specifications anymore. So you make the wing bigger, but now there's more weight and drag, so the range goes back down and probably the cruise speed, too. As a designer, you eventually end up feeling like you're chasing your own tail and getting nowhere. It's very frustrating. You start thinking, "There has to be a better way!" My first impulse when I reached this stage myself was to look for some "airplane design software" that would somehow magically tame the process and fill in for my obvious lack of experience and knowledge. My search was a disappointment. It turns out that no such animal exists. Sure, there are various spreadsheets and even programs available, but I was consistently warned that they were of limited utility and that I still had to have the knowledge necessary to do the job manually if I was going to be able to use them properly and be able to judge and trust their output.

    Let me understate and say that this was not what I wanted to hear.

    Somewhere along this progression, I heard of this guy named Dan Raymer who had a book entitled, Aircraft Design: A Conceptual Approach. I was, at this time, progressing into my career as a graphic designer, and "Conceptual" caught my eye. I recall being told that this book described the methods the aerospace primes developed new airplanes. I was collecting books at the time, looking for the magic formula that would solve all my problems and make it "easy", so I ordered the book and, when it arrived, cracked open the cover. And... was hopelessly confused.

    This guy Raymer was talking gibberish like he could tell what the airplane would weigh, how much fuel it would need, and how he could optimize things like aspect ratio and wing loading to exactly the values that would be perfect to a given set of specifications, with only a raw sketch of the airplane at best, or even none at all. On the one hand, it seemed entirely and completely backwards. How could you know the empty weight of an airplane you hadn't even drawn yet? But the part about optimizing the airplane all at once caught my attention. That was what I was hoping to do.

    The long and short of it is that I read through the text, more than a couple of times, and came to understand this process called "sizing", which was the semi-magic portal to designing an airplane for which I'd been searching. By means of mathematical relationships and statistical reference to similar designs, it's possible to learn, from the requirements and specifications, much about an airplane for which you haven't even started sketching. It's not that you're determining what this unknown design weighs, how big its wings have to be, and so on. Instead, based on the requirements, you discover what an airplane meeting them must weigh to meet those requirements, and how big its wings have to be, etc. The design flows from the specifications, instead of numbers flowing from a drawing that may or may not even remotely meet the requirements. It is backwards from where we all think to start. For me, it's better.

    A Note on Resources
    The first part of the process is pretty much standard, so both Raymer and Roskam present fundamentally the same method. There are differences in some of the details, particularly in how much information is given regarding the source aircraft for the statistical formulas used. Roskam is better about providing the source of the actual datapoints, which I find useful in determining how close the data is to my own design and therefore how accurate it'll be in performing the sizing process. Raymer, at other points in the process, has more elegant means of solving a given section.

    As a result, I'll be using elements from the work of both authors. Overall, I'll be following Roskam more than Raymer through the first initial sizing and trade studies. I'll note which author is the source of each portion as I start it. If you want to follow along, I'm using the 2005 edition of Roskam's Airplane Design: Part 1 - Preliminary Sizing of Airplanes as well as the third edition of Aircraft Design: A Conceptual Approach by Raymer.

    Next Post: Starting the sizing process.
     
    Last edited: Oct 29, 2014
  4. Oct 29, 2014 #24

    Topaz

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    Initial Sizing

    Determine Mission Payload Weight (Roskam)
    This one is easy. For a little airplane like this, the "payload" is the pilot and the baggage. We don't include fuel here because that's one of the values we'll be calculating soon. So this is "payload", not "useful load".

    Looking back at the specs sheet,

    W[SUB]Pilot[/SUB] = 180 lbs.

    W[SUB]Baggage[/SUB] = 20 lbs.

    So,

    W[SUB]Payload[/SUB] = W[SUB]Pilot [/SUB]+ W[SUB]baggage[/SUB]

    W[SUB]Payload[/SUB] = 180 + 20

    W[SUB]payload[/SUB] = 200 lbs.

    (Remember - I've assigned a trade study to see what effect allowing a larger pilot and more baggage will have on the airplane. That will come after the initial sizing process.)

    Next Post: Determining an initial takeoff weight.
     
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  5. Nov 4, 2014 #25

    Topaz

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    Determine an Initial Takeoff Weight (Roskam)
    This value, W[SUB]0[SUB](Guess)[/SUB][/SUB], literally starts off as a guess. Later, I'll use the sizing process to determine a more exact value, but it reduces the amount of effort if you can get "into the ballpark" as much as possible when starting that process. A good way to do that is to see what similar aircraft that have already been built weighed, so I'll look at other airplanes that are similar and see how they came out.

    Comparable Designs
    What I’m looking for here are airplanes that are roughly comparable to my airplane’s specification, and that also seem to match the philosophy of the design - in my case, an emphasis on low cost and, therefore, low weight and power. I can’t pick a design that looks like mine, because I don’t know what mine looks like yet! I’ll also look at designs that bracket mine on the high and low end of the performance spectrum, to establish valid trend lines. This list is going to be useful at several stages of the design process, so I’ve taken some time to come up with some pretty good selections, and gathered some extra information about them that will be useful later, too.

    (Note: To save myself the time of typing this data into tables here on HBA - which is dismal - I'm taking proppastie's good suggestion to post screen grabs out of my design notebook instead. Click on the image and it'll get larger.)

    [HR][/HR]

    AMS Flight Carat A
    This design brackets the high end of my specifications. It’s faster, has much longer range, and is a higher-performing sailplane.

    p1150577_800px.jpg

    Carat-A-Specs.jpg

    As BBerson noted, these specs (and more) are available at the AMS website.

    [HR][/HR]

    Monnett Moni
    The Moni brackets the low end of my specifications. Its range and speed are about right, but it is a lower-performing sailplane with the engine off. The relatively short wings and boxy fuselage are the primary reasons for this, but they allow the airplane to be considerably lighter than the Carat A. But there’s lots to like about this airplane, especially in terms of being “inexpensive.” BTW, if this looks like the ancestor of the Sonex, it's because it is. Same designer.

    Moni-3_800px.jpg

    Moni-Specs.jpg

    [HR][/HR]

    Sportavia-Pützer SFS 31 Milan
    “Just right”, said the blonde girl while the bears were out. The result of replacing the wings on a Fournier RF-4 with those from a Scheibe SF-27M sailplane, the Milan fits my specification set almost perfectly.

    SFS-31-Milan_Factoy-Postcard_Front_800px.jpg

    Milan_Specs.jpg

    [HR][/HR]

    Schleicher ASK-14
    This is another design that is very close to what I’ve described in my specifications document. In fact, given my focus upon“small, light, and inexpensive”, this aircraft, with its lower weight and small engine, is even closer to my goal than the SFS 31. It's a little slower in cruise, and the maximum rate of climb might end up being slightly low, but otherwise it's quite a good match. Unfortunately, I’m missing some information on this aircraft - especially the range under power. If anyone can provide a source to fill in the blanks, please let me know!

    ask-14-treffen-005_800px.jpg

    ASK-14_Specs.jpg

    [HR][/HR]

    Discussion
    Looking at these aircraft, and knowing that I'm going to make a big effort at keeping the aircraft light, I think it's a fair guess that the airplane will weigh somewhere in the ballpark of the ASK -14. That airplane is built of wood and, at this point, I think my airplane will be composite or a combination of composite and metal, so mine will probably be a bit lighter.

    So let's say W[SUB]0[SUB](Guess)[/SUB][/SUB] is 780 pounds.

    Next: A series of posts to determine the weight fraction of fuel required to meet the specifications.
     
    Last edited: Jul 4, 2015
  6. Nov 5, 2014 #26

    Topaz

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    Determine Mission Fuel Fraction

    Having taken a SWAG at the maximum takeoff weight of the airplane, I next need to determine the fraction of that weight that must be fuel. Sure, it's possible to express this in pounds, since I have a guess at the aircraft weight, but expressing it as a fraction is more useful as the aircraft weight goes up and down during sizing. "But the range doesn't change," you say. Quite right. But as the airplane's weight goes up and down, the power-to-weight ratio to achieve the same performance stays the same, meaning a larger or smaller engine is necessary to achieve the same performance. That bigger or smaller engine requires more or less fuel, so even though the range is a constant, the fuel required to complete the design mission isn't. Expressing the fuel weight as a fraction of the total weight of the aircraft takes care of that problem.

    Design Mission Profile
    The "Design Mission Profile" describes the most-challenging mission that the airplane must be able to accomplish in order to meet the requirements. I figured this out when developing my requirements: A 252 nm flight from Skylark Field (CA89) to Fresno-Chandler (KFCH) at a cruising altitude of 7,000' MSL. To account for headwinds and/or a diversion because KFCH might be unexpectedly closed, I added 50nm to the range requirement rather than adding a "loiter" segment that really doesn't apply. Cruising to another airport is the same as cruising to the first airport, in terms of engine power (fuel expenditure), altitude, etc. So the total range for the design mission is 300 nm. Design cruising speed is 115 knots.The fuel-fraction method breaks up the flight into major segments, and then estimates the fuel fraction required for each segment. To keep everything clear in the mind, it's useful to draw out the mission profile and mark these mission segments:


    Design-Mission-Profile.jpg

    The blue line is the actual mission profile (not to scale). There's engine start, taxi and takeoff, climb, cruise (with my "reserve" range marked as dashed), descent, and then landing and the final taxi. The green bar marks and labels each of these mission segments. At the start and end of each segment, there is a point, marked with a black circle. The first point, at engine start, is W[SUB]0[/SUB], the starting weight of the aircraft on the mission. Starting the engine, letting it warm, talking to ground control, etc., burns up a little fuel so, before the aircraft even moves, the weight has gone down a little, to W[SUB]1[/SUB]. Taxi out and especially takeoff burn yet more fuel, so by the time we leave the ground, the airplane weight is at W[SUB]2[/SUB], and so on until the mission is completed. When the engine is shut down after a full-range flight including the reserve range, there should "ideally" be only unusable fuel in the tanks, leaving the airplane at W6. For each mission segment, I'll calculate the aircraft's fraction of original weight that's remaining after fuel is burned off: W[SUB]1[/SUB]/W[SUB]0[/SUB], W[SUB]2[/SUB]/W[SUB]1[/SUB], W[SUB]3[/SUB]/W[SUB]2[/SUB], and so on. The fuel weight fraction for the entire flight is W[SUB]6[/SUB]/W[SUB]0[/SUB], giving the amount of the aircraft's weight that's empty weight and payload. The difference is fuel.

    Next Post: Calculating the fuel fraction for Engine Start and Warmup.
     
    Last edited: Nov 6, 2014
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  7. Nov 6, 2014 #27

    Topaz

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    Engine Start and Warm-Up
    Raymer lumps this segment together with taxi and takeoff, using a statistically-derived value for all of them of 0.970, regardless of aircraft type (Table 3.2, folio 20, Aircraft Design: A Conceptual Approach 3e). However, even the least time spent at the airport will show you that little airplanes tend to preflight, start the engine, and start taxiing within a few minutes, while turboprops and jets tend to start the engines and linger for quite a bit longer while the crew checks the more extensive systems, programs the flight director, etc. I think burning 3% of the aircraft's weight in fuel for engine start, warmup, taxi, and takeoff seems a little excessive for a single-seat homebuilt. I think that's especially true for a design such as mine that will deliberately use a small-ish engine.

    Roskam breaks the segments down individually, and provides statistically-derived values for twelve different airplane types. I like that, so I'm going to use Roskam's Table 2.1 (folio 12, Airplane Design: Part 1: Preliminary Sizing of Airplanes) for these segments.

    For a homebuilt, that source lists a segment weight fraction of:

    W[SUB]1[/SUB]/W[SUB]0[/SUB] = 0.998

    Taxi and Takeoff
    Again using Roskam's Table 2.1 for "homebuilts", I get a segment weight fraction for taxi of 0.998 and the same value for the takeoff run and climb to 50 feet AGL.

    Multiplying them together gives the weight fraction for the "Taxi and Takeoff" segment of my mission profile:

    W[SUB]2[/SUB]/W[SUB]1[/SUB] = 0.996

    Next Post: Calculating fuel fraction for climb.
     
    Last edited: Nov 7, 2014
  8. Nov 8, 2014 #28

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    Climb
    There's a notation under Roskam's Table 2.1 that says, "The numbers in this table are based on experience or on judgement. There is no substitute for common sense! If and when common sense so dictates, the reader should substitute other values for the fractions suggested in this table."

    Yep, gonna do that now.

    Roskam suggests a weight fraction value for homebuilts, for the climb, of 0.995. For single-engine certificated aircraft, he suggests 0.992. Raymer, for takeoff and climb together, suggests 0.987. I think the difference in Roskam's two values reflects differences in the historically most-typical flight usage for homebuilts and certificated aircraft: local "fun flying" and longer cross-country flights, respectively. The latter generally means a longer climb, with the engine spending more time at high power setting. Raymer's number probably also reflects this, with the addition of much larger transports and fighters being included in his data.

    For the design mission, my airplane is operating much more like a certificated cross-country airplane. Even though the range is short, I have a climb to 7,000' MSL that's higher than that for the typical "$57 burger" flight. So I think I need to use a different climb fuel weight fraction than Table 2.1 would suggest.

    I think the value for single-engine certificated aircraft better reflects how my airplane will be used on the design mission, so that's the value I'll use.

    W[SUB]3[/SUB]/W[SUB]2[/SUB] = 0.992

    Next Post: Fuel fraction for cruise.
     
    Last edited: Nov 12, 2014
  9. Nov 15, 2014 #29

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    Interlude - Life Happens.

    Sorry for the extended delay in moving this forward. Having some more "life issues" going on, and my focus has been there. Back to it soon.
     
  10. Jun 6, 2015 #30

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    Cruise
    For most sport aircraft, and especially “cruising” designs meant for long cross-countries, this is most critical part of the sizing effort. A substantial portion of the takeoff weight of such aircraft is fuel. My design has a very short range in the scheme of things: just 250 nm. This makes the weight fraction determination for cruise less critical, and highly accurate estimation less important - errors will have less effect on the final sized weight of the aircraft. Which is a good thing, because the fact that this aircraft is a motorglider makes it considerably more complicated.

    Conventional sportplanes, smaller general aviation aircraft, and propeller-driven airliners get their best range when cruising at the airspeed corresponding to the maximum L/D ratio of the aircraft. Makes sense - you’re carrying the weight weight of the aircraft at the minimum amount of drag. (There’s a peculiarity of jet aircraft that makes them get best range at an airspeed somewhat above best L/D, but that doesn’t enter in to the discussion here.) The better the L/D, the better the cruise performance of the airplane.

    So we look at the DS54 spec sheet and say, “Sweet! This airplane will be getting an L/D of 30:1! This airplane will hardly need any fuel at all for this short range!” And that would be true, if we don’t mind getting to the destination in half of forever. See, gliders can get a really high L/D, but only the most-sophisticated, highly-advanced competition sailplanes get that high L/D at an airspeed anywhere near the cruise speeds of even modestly-performing sportplanes. Most get their best L/D at about the cruise speed of a Cub. What happens if you use an engine to push the motorglider faster? Take a look at the graph below, which happens to be the L/D curve of the DS43 flying plank sailplane I worked on some time back. (You can see that airplane here.)

    DS43-L-D-Curve.jpg

    That airplane gets its best L/D of 25:1 at about exactly 50 mph. Below that speed, increasing amounts of induced drag lower the L/D value. Above the best-L/D speed, induced drag drops off, but parasite drag is increasing, and enough that L/D begins to drop off again. The best-L/D speed is that speed where the sum total of induced and parasite drags is at a minimum.

    What does this mean for a motorglider, and what does it mean for my DS54 here? My design cruise speed is specified as being in the 92-132 mph range (80-115 knots). That’s almost certainly going to be significantly above the best-L/D speed of the aircraft, so obviously I’m not going to get an L/D of 30:1 at cruise. However, the equations for fuel fraction during the mission cruise segment require an L/D value for the aircraft in that mission segment.

    My job in this segment of the work is to estimate an L/D value for the airplane at its cruise speed, not the best L/D of which the aircraft is capable. On my two-seat project, I really beat my head against the wall (entirely excessively) during this early stage of the sizing process, because that airplane has a longer range and I wanted to “get it right”. Because this airplane has a much shorter range and I’ve learned more about how the later sizing efforts are more important than this first pass, I’ll be doing a much more “quick and dirty” L/D estimation here.

    Next Post: Estimating Cruise L/D value.
     
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  11. Jul 1, 2015 #31

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    This post continues the discussion of determining mass-fraction for the aircraft on the cruise leg of the mission.

    Estimating Cruise L/D[SUP]1[/SUP]
    In my last post, I discussed why motorgliders generally don’t get great L/D values in powered cruise: They fly faster than their best-L/D speed. My next task here is to estimate the L/D of the DS54 at cruise. Here we go.

    Because this aircraft has such a short design range, and because absolute accuracy isn’t necessary at this stage of development, I’m going to cheat and use the L/D curve from one of my DS43 variants for this purpose. When I was working on the DS43, I explored some variants with more soaring performance than the baseline version. One of them looked at the maximum performance potential of the design (within some constraints) and the L/D curve of that variant comes pretty close to what the DS54 will probably have:

    DS43+-L-D-Curve.jpg

    (You’ll note that for my purpose today, I’ve opened up the top end of the speed envelope to encompass what the DS54 is expected to do.)

    Now let’s use this to estimate DS54 L/D at the design cruise airspeed. This is conservative since, at any lower speed, the L/D will be better and the range on a given fuel load will be longer. The DS43 tops out at about 27:1 and, because of its low wing loading, the L/D[SUB]max[/SUB] occurs at a fairly low airspeed. I’m pretty sure the DS54 will have a somewhat higher wing loading, and the goal L/D[SUB]max[/SUB] is slightly higher. If I plug the DS54 design cruise speed (132 mph) directly into the curve, I get an L/D of about 8:1. Adjusting for the higher maximum L/D and slightly higher speed at which it occurs, I roughly estimate L/D[SUB]cruise[/SUB] to be about 11:1. Down from 30! Still, that sounds about right. and it’s why it’s important to make this estimation for a motorglider.

    Estimating cruise weight fraction
    I prefer how Raymer presents this material so, if you’re following along in his book, this is Eq. 6.12 on folio 117 of the Third Edition of Aircraft Design: A Conceptual Approach. The equation is a rearrangement of the classic Breguet Range Equation, and for fps (SAE) units is written as follows:

    W4/W3 = exp((-R*C[SUB]bhp[/SUB])/(550*n[SUB]p[/SUB]*(L/D)))

    Where:

    R = Range (Remember units! This is expressed in feet!)[SUP]2[/SUP]
    C[SUB]bhp[/SUB] = Specific Fuel Consumption (Again, units. C[SUB]bhp[/SUB] is expressed in hours. Divide by 3600 to express in seconds.)
    n[SUB]p[/SUB] = Propeller efficiency
    L/D = Lift to Drag Ratio

    For my case:

    R = 345 sm (288 sm desired range, plus 57 sm “reserve”) * 5280 feet per mile = 1821600 feet.
    C[SUB]bhp[/SUB] = 0.43 (This is about the best C[SUB]bhp[/SUB] value I could find for a "generic" small engine at cruise.) / 3600 = 0.00011944
    n[SUB]p[/SUB] = 0.78 (Assuming a decent wood prop.. Metal and composite props could do better.)
    L/D = 11

    Plugging these into the equation:

    W4/W3 = exp((-1821600*0.00011944)/(550*0.78*11))

    From this I get an answer of W4/W3= 0.955

    ------------

    [SUP]1[/SUP] Remember: If you're doing a straight piston-powered sportplane, you don't have to do any of this L/D[SUB]cruise[/SUB] nonsense. Your plane will cruise at its L/D[SUB]max[/SUB]. Both Raymer and Roskam provide methods of estimating this value.

    [SUP]2[/SUP] It's been my experience that, if your solutions aren't coming out as reasonable values (and your cross-check to known values is also coming out wrong), the single most-likely culprit is improper units. Ideally we'd do a full unit analysis for every equation (and my HP 50g calculator can do it), but that's pretty onerous. Excel doesn't allow it at all. My method is to run "known" example values through all my equations first as a cross-check, then run my own data once the cross-check comes out "right". If I'm really stumped, I'll do the unit analysis on the 50g. YMMV.

    Next post: Determining mass fraction for descent-to-landing.
     
    Last edited: Jul 1, 2015
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  12. Jul 2, 2015 #32

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    Descent to Landing

    For those of you following along in Raymer or Roskam, you'll note that I'm not doing a "loiter" mission segment. Private airplanes rarely "loiter" in the true meaning of the word, and instead a lot of designers use this segment for the "reserve" range or duration beyond the cruise segment. Instead, I've just added some range to my desired cruise, on the theory that the most likely scenario requiring a "reserve" would be a diversion to another airport. As such, I'd most-likely simply be extending my cruise segment to that alternate. YMMV, of course, depending on the mission of your design.

    Moving on to the next segment, descent to landing, this is another one where simple statistical averages by aircraft type are more useful than trying to calculate a number. Roskam and Raymer agree pretty closely, and their values come in pretty much the same for homebuilts as the value for climb. How can that be, when in climb the engine is running close to full power? In the case of homebuilts, we tend to descend at a slower rate than we climb, so a descent from a given cruise altitude takes longer than the climb to that altitude, so the engine is running longer in this segment, albeit at a lower power setting. You probably still use a little less gas in descent anyway, but add in pattern time, getting diverted around that nut who cut into the pattern, etc., and the difference probably comes out as a wash. Certainly close enough for our purposes right now.

    So, looking at Roskam's Table 2.1, on page 12 of Airplane Design, Part 1: Preliminary Sizing of Airplanes,

    W5/W4 = 0.995

    Next Post: Mass fraction for the landing mission segment.
     
    Last edited: Jul 2, 2015
  13. Jul 2, 2015 #33

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    Landing

    The last mission segment is the landing and taxi-back. Again, this is generally taken from statistical data.

    Roskam calls this segment as W6/W5 = 0.995. Looking at the other segments, this seems a little high to me, given the operations I've flown myself. Landing and taxi-back consume as much fuel as climb or descent? Not in the flying I've done, and intend to do. Roskam himself suggests using common sense for your particular situation when pinning down these values, so I'm going to adjust this last mission segment a bit, consuming less fuel.

    W6/W5 = 0.997

    Next Post: Calculating the Whole-misssion Fuel Fraction
     
    Last edited: Jul 3, 2015
  14. Jul 3, 2015 #34

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    Calculating the Mission Fuel Fraction

    Totalling up all the individual fuel fractions, we get:

    W6/W0 = 0.998*0.996*0.992*0.955*0.995*0.997

    W6/W0 = 0.934

    So, what this means is that, when the engine is shut down at the end of the design mission, the airplane will weigh 93.4% of what it weighed when the engine was started at the beginning, assuming the fuel tank was full at that point.

    Or, to put it another way, the fuel used in the design mission weighs...

    Wf/W0 = 1-0.934

    Wf/W0 = 0.066

    ... 6.6% of the aircraft's maximum takeoff weight.

    In a perfect world, that'd be all we need to do. Unfortunately, there is always some small amount of fuel left in the tank and other parts of the fuel system when the engine runs out of gas. That's called "unusable fuel", and we have to carry it around, too, in addition to the fuel that will be used to fly the mission. Dan Raymer generalizes the weight of the unusable fuel as about 6% of the total fuel used, and I've got no reason to doubt him. So, taking that into account...

    Wf/W0 = 1.06*(1-0.934)

    Wf/W0 = 0.070

    Regardless of how large or small the airplane is, the fuel will weigh 7% of the weight of the aircraft when the engine is started at the beginning of the mission.

    Next Post: Determining the Power-to-Weight Ratio
     
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  15. Jul 4, 2015 #35

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    Happy "observed" Independence Day, fellow Americans! My business is essentially shut down today in observance of the federal holiday, and the things that have been making my life so crazy busy the last few months are finally easing for the moment, so I've had more time to work on the airplane. This'll be it for today, and I hope you all have a great 4th and, to everyone on HBA, a great weekend!

    Power to Weight Ratio
    Another piece of information I need to estimate, in order to size the airplane, is the power to weight ratio. If you've decided on a specific engine, this will change during sizing, and there are "fixed engine" sizing methods that account for this. I haven't chosen an engine yet, so I'm using what Dan Raymer calls a "rubber engine" sizing - the power to weight ratio is held constant, meaning that performance is held constant as the airplane grows or shrinks during the sizing process.

    The easiest way to get power to weight ratio is to look at similar airplanes that have similar performance to what I want. That's easy, since I have a list of such airplanes already compiled above.

    The two aircraft closest to my goals are the Schleicher ASK-14 and the Sportavia-Pützer SFS 31 Milan, as I noted earlier. It's easier to write down weight-to-power ratios ("power loading") instead of power-to-weight (all those decimals!) and then invert them in the formulas later, so I'm matching Raymer in that way. The weight-to-power ratios of these two aircraft are:

    ASK-14 = (W0/hp) = (794/26) = 30.52 lbs/hp

    SFS 31 = (W0/hp) = (946/39) = 24.26 lbs/hp

    As a quick statistical "reality check", Raymer has Table 5.4 (folio 90[SUP]1[/SUP] in the third edition of Aircraft Design: A Conceptual Approach), with an associated equation:

    P/W = a*V[SUB]max[/SUB][SUP]C[/SUP]

    On Table 5.4, for powered sailplanes, I get

    a = 0.043

    C = 0

    V[SUB]max[/SUB] = 145 mph (this is from my specifications list)

    So, P/W = 0.043*145[SUP]0[/SUP] = 0.043

    ... which gives a weight to power ratio of:

    W0/hp = 1/0.043 = 23.26 lbs/hp

    That's interesting, in that it implies that the powered sailplanes in Raymer's statistical sample are a bit more powerful than the two I've chosen as "close" to my own desired airplane.

    Here's another judgement call: What to choose as a design value. The consequence of going to a higher power loading is a slower climb and cruise, but I'll also get a smaller, less-expensive engine in the bargain. The sizing of the airplane will make sure that it meets all my requirements, and both of my "close" examples seem to have adequate performance for my needs. It's pretty hot here during the summer, and I've set some rather challenging requirements related to density altitude and takeoff performance, so I'll keep to the more-powerful end of the range.

    Let's say W0/hp = 25 lbs/hp and have done.

    I’m sure you guys with big Lyc’s and such are aghast at such a high power loading, but remember the long, skinny, wings this airplane is going to have. It’ll climb just fine, although takeoff acceleration isn’t exactly going to be neck-snapping!

    ----------------

    [SUP]1[/SUP] This is me being a pedantic typesetter and book layout designer. Technically, a "page" or "leaf" is a given piece of paper in a book, upon which text and images are printed on each side, which latter is called a "folio". I know the rest of the world calls each side a "page" and refers to "page numbers", but in my world, each side is a "folio" and those are "folio numbers". I do this stuff for a living and it's stuck in my blood. Deal. :grin:
     
    Last edited: Jul 4, 2015
  16. Jul 28, 2015 #36

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    Wing Loading
    Next up is to determine the minimum wing loading needed to meet certain performance requirements on my list. The way this works is that, for each performance requirement and given some known characteristics of the airplane, the maximum wing loading can be calculated to meet that requirement. The lowest wing loading will be the one that meets all the requirements, so that's the one I'll pick for the initial sizing. (The wing loading and aspect ratio will be optimized during the final sizing, so these are preliminary numbers.)

    You'll note that this is going to be another loading ratio - the parameter involved compared to the weight of the aircraft. Since I don't yet know what the W[SUB]0[/SUB] weight will be, doing it this way allows the wing area and power required to be quickly determined once the W[SUB]0[/SUB] is pinned down during the sizing.

    Like Raymer, I’ll start off by looking at the two aircraft I think are comparable to my emerging design:

    Historical
    First off, what's the W[SUB]0[/SUB] wing loading for my "comparable" designs? Pulling data for those aircraft gives:

    Sportavia-Pützer SFS 31 Milan: 7.3 pounds per square foot

    Schleicher ASK-14: 5.8 pounds per square foot.

    Those are fairly close together, in the scheme of things, and the average of the two of them is 6.6 psf. Since these airplanes are so similar to what I want in performance, I can reasonably expect the wing loading of my design to end up in this range. To keep the wing size down and improve the ride on powered cross-country trips, I'm definitely interested in keeping the wing loading up in the higher end of the range, closer to the SFS 31 than the ASK-14.
     
  17. Aug 1, 2015 #37

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    A quick note: This process of figuring out the wing loading is going to be the first opportunity to look at how my requirements list drives the design: Do any of the requirements unduly influence the airplane? Can I relax one or more requirements and get an better overall airplane? You can do all of these calculations by hand, or by a scientific calculator, but putting it all in an Excel spreadsheet makes it really easy to play with the values and find the best balance of refined requirements for the aircraft. I’m going to write this up as if I’m doing it right now, real time, but in reality I spent about three days building up my spreadsheet, testing it, and then modifying it as I went through the process of adjusting my requirements. I’ve attached an MS Excel copy of the first half of the finished spreadsheet below (I built the original in Google Sheets), covering the material here in this post. The balance will be posted at the end of the “Wing Loadings” section of posts. The sources and equations for the work below are notated in the spreadsheet itself. All the usual caveats apply: I am not a professional aerospace engineer and, while I checked the spreadsheet against the aerobatic homebuilt example in Raymer's Aircraft Design: A Conceptual Approach, it may still contain significant and even dangerous errors. If you decide to use it, check your answers by some other, independent, means and definitely realize that you're using at your own risk! If someone discovers an error I've made in the spreadsheet, please do me a huge favor and let me know in the discussion thread for this project. The link for that is below, in my signature line.

    Stall
    In the process of setting up my spreadsheet, I realized that I could’ve done a much better job in setting up my requirements for stall speed. If you'll recall, I set the threshold stall speed to be the LSA requirement of 52 mph (45 knots), to be achieved under sea-level standard conditions. The goal stall speed is to be 36 mph (31 knots), at Skylark Field (CA89) on an 80°F day, for a density altitude of 3,104' MSL. Thinking back through this, it's probably better (and definitely simpler) to keep all my takeoff-related requirements under the same flight conditions, excepting the LSA-specified requirement that I want to check against. So that's what you'll see me do here. I've updated my requirements document accordingly. I won't show it all here, but when I ran the finished spreadsheet for the takeoff calculation, I found that Hemet-Ryan was more realistic than Crystal, whose extremely high density altitude proved to be just nasty under the conditions specified, unduly driving too low a wing loading. Accordingly, all my stall/takeoff/initial climb performance requirements are going to be for Hemet-Ryan on a 95°F day.

    I've set up the stall/takeoff/initial climb flying conditions in the upper portion of the spreadsheet, and chosen a likely total wing maximum lift coefficient of 1.1. Remember, I don't really want to use flaps, and wing C[SUB]L[SUB]max[/SUB][/SUB] is going to end up being less than the airfoil's maximum lift coefficient because of 3D effects.

    For my goal stall speed of 36 mph and the high density-altitude conditions I've specified, I get a wing loading of:

    W/S = 3.2 pounds per square foot.

    Wow, that's low. Way too low. Clearly I'm not going to make my desired goal stall speed under these conditions. What happens if I switch to the threshold goal: 52 mph at sea-level-standard conditions? (The way I set up the spreadsheet, I have to adjust the "hot and high" stall speed until the sea-level-standard stall speed calculated below it hits 52 mph.) This time, the spreadsheet spits out:

    W/S = 7.5 pounds per square foot.

    Much better! So what I've learned here is that my goal stall speed requirement is too aggressive. I can reach my threshold requirement without flaps, but it's still pretty fast. I'll keep this for now, and see what happens in the other sections.

    Takeoff
    This one takes into account not only the wing loading, but also the power loading, which I calculated previously at 25 lbs/horsepower. There are other factors, such as rolling friction from the runway surface, and so on. However, my takeoff specification is a paved runway, so I can use Raymer's method directly. In the spreadsheet, the values from the stall calculation are carried over, so all I need is Raymer's "Takeoff Parameter". Looking up my takeoff run specification, I chose Hemet-Ryan's Runway 22, of which I allowed myself to use 1,227' to get to 50' altitude on takeoff. Looking up the takeoff parameter on the “50’ Altitude” curve in Figure 5.4 of Aircraft Design: A Conceptual Approach, I get a value of 140. Plugging that into the spreadsheet gives a result of:

    W/S = 4.5 psf.

    Ugh. This density altitude requirement has hit me twice now. If I relax my takeoff distance goal to the threshold value of 1,640' at 50' altitude, how does it look? That distance is still less than the actual, total runway length (2,054'), so we're okay there. Figure 5.4 gives me a takeoff parameter of 180, which gives a wing loading of:

    W/S = 5.8 psf.

    No, that's still too low. It's equal to the ASK-14, but I want a higher wing loading than that. Time for a good think!

    There are three ways I can improve the takeoff performance of the aircraft at a higher wing loading:
    .
    1. Decrease the power loading (increase the installed power), which means the airplane accelerates to takeoff speed faster, using less runway.
    .
    2. Ease off on the density altitude portion of the requirement, which gives more lift earlier, again allowing the airplane to take off in less distance.
    .
    3. Lower the stall speed, and therefore the takeoff speed. The aircraft accelerates at the same rate, but gets to a lower takeoff speed faster than a higher one, so the takeoff distance is, again, reduced.​
    .
    Let’s look at those options.

    Decreasing the power loading means a bigger engine. The engine is one of the single most expensive portions of the airframe, so I really don't want to do this. My cost goal is tough enough as it is!

    Can I realistically ease off on the density altitude goal? Hemet-Ryan is going to be one of my primary airports. For reasons it’s not important to go into, I expect to be operating from Hemet-Ryan regularly instead of Skylark, which I probably won’t use much at all. So I really need to operate well from Hemet-Ryan. The kicker is that the high density altitude conditions I'm specifying really aren't all that unusual for this place in a California summer. If I relax this requirement, I pretty much cut out the middle of the day for my flying, or at least taking off. I don't think easing this requirement is realistic, no matter how much it mends this wing-loading problem.

    That leaves lowering the stall speed, and that pretty much means flaps. I really didn't want to go here. Flaps mean added weight and complexity for the wing. However, my airplane's stall speed is already right up against the threshold goal, and it can't even meet my threshold takeoff goal without a lower wing loading than I want. Adding flaps would help both problems and, since I'm not completely out of the ballpark for either requirement, they can be very simple plain flaps that only have to go down 10-15 degrees. If I also droop the ailerons with the flaps, or go to full-span flaperons, 10 degrees is probably enough. (As a powered sailplane, the aircraft will already have drag brakes, so I don't need flaps to go all the way down to create a lot of extra drag.) This seems like the better compromise out of all three options, so that's what I'm going to do.

    For full-span flaps and drooping ailerons, with small deflections, I can probably get a wing C[SUB]L[SUB]max[/SUB][/SUB] of about 1.45. (I actually researched this a bit, but it would be a distraction to discuss it here. Suffice to say that I did it, and we can go over it in the discussion thread if you want. Of course, I'll calculate out all the flap deflections and such later, to make sure I can really reach that lift coefficient with that setup.) Plugging that back into the spreadsheet, I find that I can get the flaps-down stall speed at Hemet-Ryan, "hot and high", down to 48 mph, keeping the flaps-up sea-level-standard stall speed at an LSA-compliant 52 mph with a wing loading of:

    W/S = 7.6 psf.

    Keeping the takeoff parameter at the threshold-goal-derived value of 180, I get a revised maximum wing loading to meet the takeoff requirement of:

    W/S = 7.6 psf.

    Awesome. In a happy coincidence, the stall and takeoff maximum wing loadings came out exactly the same. Neither condition is dominating the selection of wing loading, and they're both right about where I want the wing loading for this design. Flaps turned out to be a very good solution.

    The spreadsheet for the work above can be downloaded from this link: https://app.box.com/s/mnnucxtxytgv15pkurqutj85gx6plj19

    Next Post: Continuing to calculate necessary wing loadings, for initial climb, best-L/D glide, minimum-sink glide, and cruise.
     
  18. Aug 3, 2015 #38

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    Next on the list of critical wing-loadings to determine is the initial climb rate and the two soaring metrics: Best L/D glide and minimum-sink glide.

    It turns out that these three are variations on the same situation, where you're determining how excess thrust available translates into vertical performance. The two glide cases are simply zero-thrust cases, with a negative "climb rate". The same formula is used for all three, and determining the wing loading necessary to reach each performance parameter is a matter of simply entering the characteristics of that particular situation.

    Initial Climb
    A sustained rate of climb is important for reaching cruising altitude in a hurry, so you can get up to cruise speed and make some miles as soon as possible. Initial climb is all about clearing those trees and wires off the end of the runway. The first is about economics, the second is about flight safety. As such, and as noted when I set up the specifications for this design, both certification standards are about getting above those trees in a safe amount of time.

    For the initial-climb wing loading, I pulled the FAA Part 23 climb gradient requirement and applied it to the same stall/takeoff/initial climb conditions (hot-and-high at Hemet-Ryan airport) as I used for the stall and takeoff numbers. In sea-level-standard conditions, the airplane will do much better, but this is my worst-case condition. The spreadsheet section for this calculation pulls all the necessary numbers from the previous work, and I manually added the climb-gradient spec from FAR 23.65: 0.083. This calculation also requires an estimate of C[SUB]D[SUB]0[/SUB][/SUB], and I used Raymer’s technique from Figure 3.5 and Table 12.3, resulting in a C[SUB]D[SUB]0[/SUB][/SUB] of 0.020 in the initial climb configuration (gear down, flaps down 10°-15°, power on, engine cooling doors open).

    After much number-crunching and cross-checking on this formula (I always get it typed in wrong the first couple of tries, and have to cross-check until I know it's right - when you see it in Raymer, you’ll understand), I get a result of:

    W/S = 37.7 pounds per square foot.

    Seems high, I know, but this is a result of the long wings of this airplane, which cut the power-required due to induced drag quite a lot compared to your average short-winged sportplane. As a cross-check against the CS 22.65 requirement, which specifies a climb rate to 50’ AGL, I also have the spreadsheet translate the FAR 23.65 climb gradient at the speed the aircraft will be flying (~1.4 x V[SUB]s[SUB]1[/SUB][/SUB]) into a climb rate under the same conditions. That comes out as:

    V[SUB]v[SUB](initial)[/SUB][/SUB] = 491 feet per minute.

    Not at all spectacular but, for these high density-altitude conditions, good enough. Hemet-Ryan is flat for miles in the takeoff direction, so flight safety is not a factor here. The climb-rate result is better than the CS 22.65 requirement, so we’ll call this one “good” and move on.

    Best L/D Glide
    As I mentioned, this is exactly the same formula as the initial climb calculation, power off, and with the “climb” gradient being simply the desired L/D ratio converted to a gradient. Doing this results in a negative “climb” gradient - the airplane is going down, not up.

    The only other modification is that the airplane isn’t in the same conditions or configuration as it is for stall/takeoff/landing. The engine is off, cooling doors close, flaps retracted. Gear is still up. Soaring conditions are highly variable, and it’s not really that critical to safety to get maximum soaring performance all the time (after all, I have an engine upon which to fall back, if necessary), and I had to pick something, so I’m specifying that all soaring performance metrics will be assumed to be under ISO standard conditions for a pressure altitude of 3,500’ MSL. If that seems arbitrary, it’s because it is, beyond being a common "get me up" soaring altitude at Hemet-Ryan. If I were designing a competition-class racing sailplane, I’d definitely be putting more effort into these numbers, but this is a “fun” flyer, and it’s not worth the extra work to make it that precise at this stage.

    Plugging the goal L/D[SUB]max[/SUB] of 30:1 into the spreadsheet gives a maximum wing loading of:

    W/S = 11.6 pounds per square foot

    Nice. Seems like the outlier so far is initial climb rate, and it’s an outlier in the direction I want: More performance than my minimum needs, without impacting the wing size of the airplane.

    Minimum-Sink Glide
    This is almost a direct re-hash of the previous calculation, except that the requirement is couched in terms of a descent rate instead of a gradient. Easy enough to translate that rate into the gradient I need (spreadsheet does this), and voilá, I get a wing-loading result of:

    W/S = #NUM!

    This is my spreadsheet’s not-so-subtle way of telling me that there is no numerical solution for the equation with the values entered - the wing loading necessary to meet my goal requirement would be less than zero. (Yes, I’m a bad programmer and didn’t trap the error with an explicit warning.) Clearly a wing loading of less than zero is not going to do, and I’ll need to relax this requirement. After some trial and error, I found that specifying a best-minimum-sink rate of -160 fpm results in a wing loading of:

    W/S = 11.2 pounds per square foot

    While not meeting my goal specification, -160 fpm is well inside my threshold specification of -196 fpm, so we’ll call this one “good” as well, and see if I can’t get a little of this performance back later on in the wing optimization.

    Cruise, Maximum Range
    Because of the unusual nature of this aircraft - it cruises well below its best L/D, but still above most sport aircraft, this calculation is going to be a bit of an issue. However, what this calculation does is give you the wing loading necessary to give you best range for this aircraft, for whatever amount of fuel it has on-board - it’s more a measure of fuel efficiency than anything else. As such, and since my range requirement is rather tiny, I’ll only worry about this result if the wing loading it spits out is fairly close to my current minimums. If you’re doing a long-range aircraft that cruises at its best L/D, where ability to reach a specific maximum range with a minimum of fuel expended is important, pay more attention to this one. For my case, typing in the cruise speed goal specification gives:

    W/S = 35.0 pounds per square foot.

    Not a problem.

    Choosing an Initial Wing Loading
    Picking the initial wing loading is now a simple matter of choosing the one that’s most-critical. That is to say, the lowest wing loading of this series, since it makes the wing the largest. Looking down the list, the lowest wing loading cases are for stall and takeoff, both at:

    W/S = 7.6 pounds per square foot.

    That value fits nicely with historical precedent (always a good reality check) and is at the high end of that historical range - desireable for me since I trying to keep wing area down for reasons of build-space and possible trailerability, not to mention construction cost.

    The complete spreadsheet for all this wing loading work is linked here. All the caveats I listed about using it in the previous post still apply.

    Next Post: Calculating the empty weight fraction coefficents and (finally) running the initial sizing.
     
  19. Aug 20, 2015 #39

    Topaz

    Topaz

    Topaz

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    Sizing the Airplane
    Here it is, magic time! I’m going to learn a lot about my design in this next step, which is “sizing” the airplane. In the last few sections, I’ve established mathematical relationships for various parameters of the airplane, based on my specific performance requirements and historical data from aircraft that should be very similar to mine. These relationships can be used to determine the lightest aircraft that will meet my design requirements. It would be possible to build a larger, heavier airplane that would also meet the requirements, but the lightest airplane will cost the least to build and burn the least amount of fuel during the design mission, and so be the lowest-cost option. Low cost is is one of my top-level design goals, so this is important.

    (As with the wing-loading determinations above, I’ve created a spreadsheet to speed the calculations, but I’ll show most of the math here as well, for clarity. The spreadsheet can be downloaded from the link at the bottom of this post, if you want.)

    There are two kinds of sizing: Fixed-engine and “rubber”-engine. The former presumes that an engine has been chosen, and that the power loading will change as the airplane is sized up or down. For that to work, some design parameter must change, and it’s usually range. A rubber-engine sizing assumes that the power loading remains the same as the airplane sizes up or down, and so the engine power will change, leaving the other parameters intact. I tied W[SUB]fuel[/SUB] to W[SUB]0[/SUB], so that takes account of the larger or smaller engine consuming more or less fuel. I want to use a rubber-engine sizing, since I haven’t chosen my engine and I want to use the smallest, lightest, cheapest engine that will do the job, which essentially means the least powerful, engines being what they are. So what follows is a rubber-engine sizing. If you want to see a fixed-engine sizing, see the aerobatic homebuilt example in Aircraft Design: A Conceptual Approach.

    First, let’s collect a little data from my earlier work above, that will be needed for the sizing:

    Aspect Ratio: 17.6

    Wing Loading: 7.6 psf

    W[SUB]0[SUB]guess[/SUB][/SUB]: 780 lbs.

    Payload: 210 lbs.

    Total Mission Fuel Fraction: 0.070

    V[SUB]max[/SUB]: 126 knots

    The first step is to define an equation that expresses the empty weight of the airplane versus W[SUB]0[/SUB]. This isn't a fixed formula for all airplanes - it varies by aircraft type. That makes sense, in that a little high-powered aerobat probably won't have the same empty-weight fraction as a long-winged, no-engine sailplane, or my long-winged, little-engine motorglider. The best way to do this is using historical data from similar airplanes, with a curve-fit formula to that data. Raymer puts this formula above Table 6.2, which is on folio 116 of the third edition of Aircraft Design: A Conceptual Approach. This is a curve-fit equation based on data from real-world airplanes. The table itself contains the coefficients and exponents to be used for particular types of airplanes.

    The formula is:

    W[SUB]e[/SUB]/W[SUB]0[/SUB] = a + b*W[SUB]0[/SUB][SUP]C1[/SUP]*A[SUP]C2[/SUP]*(hp/W[SUB]0[/SUB])[SUP]C3[/SUP]*(W[SUB]0[/SUB]/S[SUB]w[/SUB])[SUP]C4[/SUP]*V[SUB]max[/SUB][SUP]C5[/SUP]

    (They're standard definitions, but "A" is aspect ratio, and "S[SUB]w[/SUB]" is wing area, if you aren't familiar.)

    At first it seems impossible to solve this in any meaningful way, but recall that I already have numerical answers for the ratios in the middle of the equation. Looking up the appropriate coefficients and exponents for “Powered Sailplanes” in Table 6.2 gives the following values:

    a: 0
    b: 1.21
    C1: -0.04
    C2: 0.14
    C3: 0.19
    C4: -0.20
    C5: 0.05

    Plugging them into the equation, along with my known values from earlier in this post gives:

    W[SUB]e[/SUB]/W[SUB]0[/SUB] = 0 + 1.21*W[SUB]0[/SUB][SUP]-0.04[/SUP]*(17.6)[SUP]0.14[/SUP]*(1/25)[SUP]0.19[/SUP]*(7.6)[SUP]-0.20[/SUP]*(126)[SUP]0.05[/SUP]

    … which simplifies down to:

    W[SUB]e[/SUB]/W[SUB]0[/SUB] = 0.832539*W[SUB]0[/SUB][SUP]-0.04[/SUP]

    That’s the last thing I need in order to size the airplane, so let’s do that sizing now.

    To size the airplane, I make an educated guess about what the weight at W[SUB]0[/SUB] will be, then use the relationships I’ve defined to add up the empty weight and fuel load that results with the known payload:

    W[SUB]0[SUB]guess[/SUB][/SUB] = 780 lbs.

    W[SUB]fuel[/SUB] = 780*0.07 = 54.6 lbs.

    W[SUB]empty[/SUB] = 780*0.832539*(780)[SUP]-0.04[/SUP] = 497.5 lbs.

    Adding these up with the known payload (pilot and baggage):

    W[SUB]0[SUB]calculated[/SUB][/SUB] = 54.6 + 497.5 +210 = 762 lbs.

    As happened here, the resulting calculated W[SUB]0[/SUB] will not usually match my guessed W[SUB]0[/SUB]. So I plug my new calculated W[SUB]0[/SUB] into the “guess” position and re-run the calculations:

    W[SUB]0[SUB]guess[/SUB][/SUB] = 762 lbs.

    W[SUB]fuel[/SUB] = 762*0.07 = 53.3 lbs.

    W[SUB]empty[/SUB] = 762*0.832539*(762)[SUP]-0.04[/SUP] = 486.6 lbs.

    W[SUB]0[SUB]calculated[/SUB][/SUB] = 53.3 + 486.6 +210 = 750 lbs.

    Still doesn’t match, but notice that the guessed and calculated values are now closer together. The solution is converging. Now I simply plug the new calculated W[SUB]0[/SUB] back into the “guess” position, and do it all again. This is where a spreadsheet comes in really handy!

    The long and short of it is that, after about ten iterations or so, the values of W[SUB]0[SUB]guess[/SUB][/SUB] and W[SUB]0[SUB]calculated[/SUB][/SUB] have converged to the point where they’re the same within a percent or so - completely “close enough” for this stage of the game. You can see that process in the spreadsheet. The final result of the sizing is:

    W[SUB]0[/SUB] = 724 lbs.

    W[SUB]empty[/SUB] = 463 lbs.

    W[SUB]fuel[/SUB] = 51 lbs.

    If I add 210 pounds of payload to that fuel and empty weight, I get the W[SUB]0[/SUB] value of 724 lbs. This, within the accuracy of this first-order method, is the smallest, lightest, and likely least-expensive powered sailplane that will meet my requirements.

    First thing: A reality check. Math can do weird things sometimes. Does this set of weights seem realistic, based on comparable airplanes? Looking at the “comparable” airplanes in my list, I see that my airplane is rather lighter than the ASK-14 and SFS 31, both in gross and empty weight. It is, however, heavier than the Moni, by a fair amount. The Carat A is a lot heavier. What does this say about the realism in my sized airplane? Are there reasonable explanations for the discrepancies, or is it clear that something has gone awry?

    First, let’s look at the ASK-14 and SFS 31. Both airplanes are built of wood, which isn’t the stiffest, lightest of materials with which to build something long and spindly like a sailplane. While I don’t know the range of the ASK-14, the range of the SFS 31 is larger than mine, and the payload is larger. All of these factors will conspire to create a heavier “sized” airplane.

    The Moni is lower-performing than my airplane, which will mean a shorter, lighter wing, and it’s built of aluminum sheet, which is one of the lightest airplane building materials there is. The range is shorter and the payload is about the same as my aircraft. It makes sense that this airplane will be lighter than mine, but it also shows that my empty weight number isn’t completely out in left field for a small, light, single-seat motorglider.

    The Carat A has almost twice the range, a bigger payload, and more soaring performance. Yes, it should be quite a bit heavier than mine.

    So yes, I’m comfortable with the sized aircraft. Keeping the empty weight down that low will be a challenge, and it’s going to color my configuration development with the need to keep weight down a lot.

    Wrapping up Sizing
    One last “little” bit to do with the sizing: Now that I know the value of W[SUB]0[/SUB], I can figure out a lot more about the airplane using the relationships I developed earlier:

    Dividing W[SUB]0[/SUB] by the known wing loading gives:

    Wing Area = 724/7.6 = 95 square feet.

    Taking the wing area and known aspect ratio, I get:

    Span = SQRT(95*17.6) = 41 feet.

    Gasoline weighs 6.08 pounds per gallon, so my fuel tanks will have to hold (including unusable fuel):

    Fuel Volume = 51/6.08 = 8.3 gallons.

    And now, the number we’ve all been waiting for. Dividing W[SUB]0[/SUB] by the power loading gives:

    Engine Power = 724/25 = 29 horsepower.

    This is why the sizing process is so “magical” to me. All of a sudden, hard numbers about my airplane start falling out of the sky. And those numbers describe an airplane that will perform exactly how I want, based on my actual requirements. When I start drawing this airplane, I will know exactly what to draw, at least in terms of the sizes of things - the airplane was defined in numbers before I ever put pencil to paper.

    Spreadsheet for this post: https://app.box.com/s/ep2w6662z7z9j9nxp922ogq917imx3to
    (A quick note: For some reason, the preview of the spreadsheet in Box shows the wrong numbers in the sizing iterations. I'm not exactly sure why that is, but if you download the spreadsheet, it'll be fine and show the correct numbers.)

    Next Post: Choosing an engine.
     
    Last edited: Aug 20, 2015
    rtfm, blane.c and Himat like this.
  20. Aug 21, 2015 #40

    Topaz

    Topaz

    Topaz

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    Baseline Engine Selection
    I'm getting very close to exploring configurations for this aircraft (finally some drawing, I know!), so it's time to choose a baseline engine.

    What do I know about the engine I need?

    Sized Power: 29 horsepower

    Sized Brake Specific Fuel Consumption (BSFC): 0.43

    Since this is a motorglider, the ability to start the motor in-flight is necessary, since I'll be shutting it down often to do some soaring. Either electric or recoil start are acceptable.

    I may not need the engine to have an alternator. I don't want the extra weight and expense, and my desire is to use a hand-held radio as I do when soaring, and which has its own internal battery. The rest of the "avionics" are mostly mechanical, or a commercial tablet that could run off its own battery easily for the entire length of the design mission, and then some. A single small motorcycle-style battery could run my electrical system for days on end, and start the motor several times on a single charge. This reflects my sailplane experience. I'm not going to baseline an alternator. Another alternative is a plug-in wind-driven generator for powered cross-country flights, although that will be a big source of drag.

    Subjective desired qualities are "light weight" and "low cost".

    The BSFC strongly implies a 4-stroke engine, and despite the advances in 2-strokes, I'd prefer to fly with a 4-stroke for reasons of reliability and low maintenance. I'm not excluding 2-stroke engines if I can find one that meets my needs, but rather expressing a preference.

    The sized power of 29hp is an approximate bottom bound, where the airplane may not meet performance requirements if the installed power is lower. In the other direction, a substantially more-powerful engine will have a higher fuel consumption that would invalidate the sizing. There's also the reality that airplanes tend to get heavier, not lighter, as development progresses, and certainly over their working lifetimes. A little extra installed power isn't a bad thing, and the engine will be throttled back a little more at the design cruise speed, giving the same fuel consumption and prolonging its life. Adding it all together, let's say this:

    Installed Power: 29-35 hp

    Installed Brake Specific Fuel Consumption (BSFC): 0.43-0.45

    So what's out there in this range?

    The first thing that comes to mind is that there aren't any certified aircraft engines in this power range of which I'm aware. So that thought goes out the window.

    The obvious engine option is a 1/2 VW. Hummel Engines has a 32 hp model for only $2,950, ready to run (I confirmed this with Scott Casler at Hummel - their engines are ready to run except for prop and exhaust system). Add a starter and the price goes to $3,325. It's four-stroke, and I have some experience wrenching VW engines, which I consider a plus for this engine. BSFC is unstated on their website, but I pulled my original 0.43 from a VW engine in the first place, so it should be pretty close. The engine has a couple of down-sides, however: For one, it's quite heavy, at 83-103 lbs., depending on options and mount type. For another, it's an opposed twin, meaning it's quite broad and will possibly impose a drag penalty in soaring mode.

    Another option is the Hirth F-33. At 28hp, it's a single horsepower below my sized engine power needs, but at this point, that's quite close enough. The added bonus is that the engine, itself, weighs only 35 pounds! Adding a reduction drive (weight unlisted on their website) might bring the total powerplant weight up to 50 pounds or so, but the low weight is very attractive. Down-sides of this engine are that it's a single-cylinder engine (vibration), and a two-stroke. That latter is a killer, beyond my subjective fears, because I calculate the BSFC for this engine at 0.76, based on the information on the Hirth website. That's typical for a 2-stroke, and it's much too high, invalidating this engine as a choice for my airplane, despite its advantages.

    For the moment, I'm going to baseline the 32hp Hummel 1/2 VW and look further for other options. I'd like your help with this! There are enough small-engine discussions here on HBA that even using the advanced search turns up more noise than data, and I'm not really well-versed with engines in this power range. Are there any established turnkey V-twin options in this envelope? If you know of a readily-available engine in the 29-35hp range, 4-stroke, that is smaller/lighter and/or costs noticably less than the $3,325 Hummel, please let me know about it in the discussion page. HBA is only a resource if we ask, and I'm asking.
     
    Last edited: Sep 10, 2015

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