mcrae0104 project

Discussion in 'Member Project Logs' started by mcrae0104, Nov 27, 2017.

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  1. Nov 27, 2017 #1

    mcrae0104

    mcrae0104

    mcrae0104

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    Time to consolidate some loose ends.

    Those with a long memory may recall that I introduced myself on this forum thinking about this design, a tandem aluminum LSA:

    3-view.jpg

    A lot of time has passed, during which the mission, the primary material, and a lot of other things have changed. I've posted a few bits and pieces recently and received some requests to post more. I've always been hesitant about posting details but maybe the time has arrived for a real project log. Of course there have been a lot of iterations since that first sketch, but currently it looks something like this:
    August 3-view.jpg sketch.jpg IMG_6056.jpg IMG_6065.jpg IMG_6072.jpg IMG_6063.jpg IMG_6067.jpg IMG_6069.jpg


    The mission: A light, relatively simple personal cruiser with performance above the LSA class, but not a crazy stall speed for a low-time pilot like me. The majority of flying will be local, but it should be efficient enough for some good cross-country distance. Good performance at hot/high DA is a must. Construction will be plywood; quick build time is not a priority. Must be roomy enough to fit my tall frame with wiggle room for a comfortable 3-4 hour leg. Needs to carry enough baggage for a civilized weekend or an "uncivilized" week of camping at OSH. No passengers to complicate things--that can wait for a future design. This one's a personal fun/travel machine.

    Rough figures (of course subject to wild revisions, as they have undergone many iterations to date):
    • Limit load: +6/-3
    • W[SUB]0[/SUB] = 1,260 lb
    • W[SUB]e[/SUB] = 806 lb (needs to be verified as I get a little further along with structural design--I hope I can beat this figure.)
    • W[SUB]f[/SUB] = 203 lb
    • Span = 25'-6" (A = 8.0; λ = 0.5)
    • Wing area = 81 ft[SUP]2[/SUP]
    • Wing loading = 15.6 lb/ft[SUP]2[/SUP]
    • Stall speed (V[SUB]0[/SUB]) = 58 mph (assumes overall flapped C[SUB]Lmax[/SUB] = 1.8; airfoil has not been finalized but assumes GA37A15 for now)
    • V[SUB]cr[/SUB] = 149 kt IAS / 197 mph TAS @ 75% 7,500 MSL; 128 kt IAS / 147 mph TAS @ 55%, 7,500 MSL
    • Range = 597 sm @ 75%, 7,500 MSL / 749 sm @ 55%, 7,500 MSL (no reserve)
    • Power = 140 hp (turbocharged 2775cc Corvair; this figure may be optimistic but it will do as a placeholder for now)
    • ROC = 1,320 fpm (SL); 1,000 fpm 7,500 standard day

    At OSH this summer, I showed a previous version of the design to someone, who said it reminded him of the Polen Special. BJC mentioned the same thing recently. The resemblance is coincidental, but I will confess that both the Polen Special and GP-5 are among my favorites and probably have subconsciously influenced the form, as well as all of the wonderful F1 racers at Reno. One thing that is a bit unconventional is that the spar passes just in front of the rudder pedals, rather than below the pilot's knees. There is a little weight penalty (and a visibility penalty) to be paid for this, but to my eye, it makes for a more elegant design.

    Discussion thread here: https://www.homebuiltairplanes.com/forums/showthread.php?t=28827&p=410843#post410843
     
  2. Nov 28, 2017 #2

    mcrae0104

    mcrae0104

    mcrae0104

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    Why wood?

    Selecting the structural material to work with might seem like the most primary decision you make as the designer of a plane. Actually, I'm not sure it is. It's said that form follows function--or more precisely in this context, that form follows what is possible in your chosen material. But you can approximate the shape dictated by the aerodynamic design in a number of materials. Perhaps the question is, how aerodynamically perfect do you want it to be?

    Nothing makes my heart race like a polished aluminum plane. Doesn't matter if it's a 140 or a Midget Mustang. And this is where I started. But a few things bothered me. While a P-40 or P-51 could be executed in a way to mask any discontinuities, largely due to their size (or they could use hydroformed panels to avoid the discontinuities altogether), homebuilts tend to have little creases and flat surfaces that catch the eye, or worse yet, oil-can. Sure, you could design around this sort of thing by slicing up the fuselage into small enough increments that the eye--and maybe even the air--wouldn't notice. But more often, we see slab sides, sharp corners, and a sharp bend just behind the canopy as a constructability compromise.

    So why not composites? Well, I don't like that I would need to paint it white just to keep from losing strength. Initially, the engineering seemed out of reach. I knew how to design a beam in wood or aluminum, but that plastic and fiber stuff seemed otherworldly and out of reach.

    Wood, on the other hand, could be persuded to take on the shapes that the air wanted, and it didn't have to be white. Ironically, the engineering is the same as for composites, and suffers some of the same temperature concerns if assembled with epoxies, but it just feels right to me. And during the assembly process, it posesses a certain beauty unmatched by other materials. If you've seen a Falco being built, you know what I mean.

    The other thing I find appealing is the idea of building something relatively advanced (maybe from a 1940s perspective, at least) out of a dirt-simple, old-school material that could possibly be lighter than the more space-age materials. So wood it is, at least for now.
     
  3. Nov 29, 2017 #3

    mcrae0104

    mcrae0104

    mcrae0104

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    Raymer, Simplified Aircraft Design

    If you don't have a copy of Dan Raymer's Simplified Aircraft Design for Homebuilders, stop what you are doing right now and buy a copy. It won't tell you everything you need to know, but it will tell you about a great many things you need to know so that you can begin learning.

    My hope is that you will see how hard this isn't, and that you'll start your own design project and post it for us all to see.

    Here are some examples of the early sizing equations you'll work through in conceptual design. (Don't use the following as a cookbook, though--buy the book, read it, and understand it.) Some of the numbers below differ from what you see in the first post, and we'll get to that later.

    Power Loading:

    [​IMG]

    Note that V[SUB]max[/SUB] should be in knots. This equation, like many of the ones to follow, is based on statistical data. It is telling us that planes of a particular max speed and other characteristics tend to have similar power loading. It is not used to say your airplane will have a particular max speed if you give it a particular power loading. This is helping us get in the ballpark, and later when we have more figured out, we can check the performance.

    Using 200 mph as our assumption for max speed,

    [​IMG]

    Or if we assume 230 mph,

    [​IMG]

    So we'll want to be in the neighborhood of 8.5 to 9.25 lb/hp.
     

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  4. Nov 29, 2017 #4

    mcrae0104

    mcrae0104

    mcrae0104

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    Wing Loading:

    This is the lift equation:

    [​IMG]

    where:
    L = lift (lb)
    q = dynamic pressure (lb/ft[SUP]2[/SUP])
    S = wing area (ft[SUP]2[/SUP])
    C[SUB]L[/SUB] = coefficient of lift (dimensionless)

    Knowing that lift equals weight (a nearly-true assumption), we can rearrange the equation like this:

    [​IMG]

    Now you see that we have wing loading on one side of the equation (W/S). But what should we use for q and C[SUB]L[/SUB]? Let's select a stall speed of 58 mph and assume a coefficient of lift of 1.8 with flaps. Later, when we "really" design the wing, we can revise C[SUB]L[/SUB] and re-check the resulting stall speed. This is close enough for now.

    Dynamic pressure:

    [​IMG]

    where:
    ρ (rho) = the density of air (slugs/ft[SUP]3[/SUP]). A slug is the amount of mass that accelerates 1 ft/sec[SUP]2[/SUP] when 1 lb of force is exerted on it. ρ=0.00238 slugs/ft[SUP]3[/SUP] on a standard day at sea level.
    V = stall speed (ft/sec)

    [​IMG]

    (I promise that if you substitute ft/sec[SUP]2[/SUP]/ft[SUP]3[/SUP] as the units for ρ, the resulting units of q will be lb/ft[SUP]2[/SUP])

    Now plug in q and C[SUB]L[/SUB] to get:

    [​IMG]

    This seems reasonable: higher than an LSA, and pretty comparable to a lot of GA aircraft. Wing loading is just a function of stall speed and coefficient of lift.
     

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  5. Nov 29, 2017 #5

    mcrae0104

    mcrae0104

    mcrae0104

    Armchair Mafia Conspirator HBA Supporter

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    Lift-to-Drag Ratio (1):

    We've all heard of "L-over-D." The higher the number, the more efficient the plane. The sailplane guys can tell you all about it. Here is the equation:

    [​IMG]

    Let's break this down to figure out our cruise L/D. We'll figure out each of the parts and then put them all back together.

    q = dynamic pressure, this time at cruise speed
    C[SUB]D0[/SUB] = parasitic drag coefficient
    W/S = wing loading--hey, we know that already!
    K = drag-due-to-lift factor
     

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  6. Nov 29, 2017 #6

    mcrae0104

    mcrae0104

    mcrae0104

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    Lift-to-Drag Ratio (2):

    We will assume a cruise speed of 200 mph at an altitude of 7,500 MSL. ρ is 0.0019 slugs/ft[SUP]3[/SUP] up there.

    [​IMG]
     

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  7. Nov 29, 2017 #7

    mcrae0104

    mcrae0104

    mcrae0104

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    Lift-to-Drag Ratio (3):

    Parasitic Drag Coefficient, C[SUB]D0[/SUB]: also known as zero-lift drag. This is the total drag of the airplane, minus any induced drag.

    [​IMG]

    where:
    C[SUB]fe[/SUB] = skin coefficient fraction
    S[SUB]wet[/SUB]/S[SUB]ref[/SUB] = the ratio of total wetted area to to wing area (the wing area is the "reference" area)

    For C[SUB]fe[/SUB], Raymer lists these values in a table:
    Single-engine, fixed gear, average design: 0.0090
    Single-engine, fixed gear, smooth design: 0.0065
    P-51 (based on flight test data): 0.0053

    We'll be conservative and select C[SUB]fe[/SUB] = 0.00775, midway between "average" and "smooth."

    For S[SUB]wet[/SUB]/S[SUB]ref[/SUB], Raymer lists this value in a table:
    Single-engine, conventional design: 3.8.
    Once we've drawn or modeled the plane, we can check this value. We might come out better, but for now, we'll use his value of S[SUB]wet[/SUB]/S[SUB]ref[/SUB] = 3.8.

    Now, put this all back into the first equation above:

    [​IMG]
     

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  8. Nov 29, 2017 #8

    mcrae0104

    mcrae0104

    mcrae0104

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    Lift-to-Drag Ratio (4):

    For K, the drag-due-to-lift factor, Raymer lists this approximation:

    [​IMG]

    where:
    A = aspect ratio. We will select A = 8.

    [​IMG]
     

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  9. Nov 29, 2017 #9

    mcrae0104

    mcrae0104

    mcrae0104

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    Lift-to-Drag Ratio (5):

    Now, let's put it all back together. Here is what we know:
    q[SUB]cruise[/SUB] = 81.74 lb/ft[SUP]2[/SUP]
    C[SUB]D0[/SUB] = 0.0295
    W/S = 15.5 lb/ft[SUP]2[/SUP], but we'll multiply this by 0.98 since we've burned off some fuel by the time we reach cruise, so W/S = 15.2 lb/ft[SUP]2[/SUP].
    K = 0.053

    [​IMG]

    [​IMG]

    Now, if that seems low--and it does--then it probably means we've selected a speed that's too high for efficient cruising. In fact, for this design, L/D[SUB]max[/SUB] is close to 12.2 at around 80 KIAS, and at a lower cruise speed of 149 KIAS, L/D[SUB]cruise[/SUB] is about 7.35. This will certainly be better than 5.93 when it comes to figuring out how much fuel we need to carry (which, by the way, is why we're bothering with finding L/D).
     

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  10. Nov 29, 2017 #10

    mcrae0104

    mcrae0104

    mcrae0104

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    Fuel Fraction:

    The fuel fraction, W[SUB]f[/SUB]/W[SUB]0[/SUB], is a ratio of the weight of fuel we need to carry to the takeoff weight. It's the percentage of max weight that is taken up by fuel. It depends on the desired range and L/D. Calculating this will help us get to calculating the empty weight and gross weight of the aircraft.

    [​IMG]

    where:
    W[SUB]f[/SUB] = fuel weight (lb)

    W[SUB]0[/SUB] = takeoff weight (lb)

    e
    = 2.71828 (you'll remember this from high school algebra)

    R = desired range (feet)

    [​IMG]

    C[SUB]bhp[/SUB] = specific fuel consumption (lb/sec/hp). We'll use 0.5 lb/hr/hp as a pretty good rule of thumb since the actual specific fuel consumption of the selected engine isn't known.

    [​IMG]

    η[SUB]p[/SUB] = propeller efficiency. We will assume 0.75 as a start for a fixed-pitch propeller.

    L/D[SUB]cruise[/SUB] = 7.35 (as mentioned in the last post).


    [​IMG]

    Finally, we'll multiply this by 1.06 to account for unusable fuel, and find that W[SUB]f[/SUB]/W[SUB]0[/SUB] = 0.166.
     

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  11. Nov 29, 2017 #11

    mcrae0104

    mcrae0104

    mcrae0104

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    Takeoff Weight & Empty Weight Fraction:
    This is where it all comes together. When we know the takeoff weight (W[SUB]0[/SUB]), we can find the empty weight (W[SUB]e[/SUB]) using the empty weight fraction (W[SUB]e[/SUB]/W[SUB]0[/SUB]), and we can turn the power loading, wing loading, and fuel fraction into concrete numbers that are at least a reasonable starting estimate.

    [​IMG]

    where:
    a = 1.19; this is a constant that depends on the type of construction and the starting figure of 1.19 is given by Raymer in a table. This figure can be refined later after some weight estimation has been done.​

    [​IMG]

    where:

    W[SUB]people[/SUB] = 200 lb
    W[SUB]payload[/SUB] = 50 lb
    ...and we'll substitute aW[SUB]0[/SUB][SUP]-0.09[/SUP] for W[SUB]e[/SUB]/W[SUB]0[/SUB]:

    [​IMG]

    [​IMG]

    Because W[SUB]0[/SUB] (on the left side of the equation) is now defined in terms of W[SUB]0[/SUB] (on the right side of the equation), we'll have to take a series of guesses for the value of W[SUB]0[/SUB] until the equation is, well, equal.

    W[SUB]0[/SUB] guess: 1,150 lb W[SUB]0[/SUB] output: 1,232 lb

    W[SUB]0[/SUB] guess: 1,200 lb W[SUB]0[/SUB] output: 1,218 lb

    W[SUB]0[/SUB] guess: 1,225 lb W[SUB]0[/SUB] output: 1,213 lb

    W[SUB]0[/SUB] guess: 1,214 lb W[SUB]0[/SUB] output: 1,214 lb

    Bingo--W[SUB]0[/SUB] = 1,214 lb.

    Now we can plug this into the first equation above to find empty weight:

    [​IMG]
     

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  12. Nov 29, 2017 #12

    mcrae0104

    mcrae0104

    mcrae0104

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    Power Loading, Wing Loading, and Fuel:

    Now that we know W[SUB]0[/SUB] = 1,214 lb, we can find:

    Required power range, based on our pre-selected power loading range:

    [​IMG]

    [​IMG]

    Wing area, based on our pre-selected wing loading:

    [​IMG]

    Fuel capacity
    ,based on the fuel fraction:

    [​IMG]
     

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  13. Nov 30, 2017 #13

    mcrae0104

    mcrae0104

    mcrae0104

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    You may have noticed that the numbers we came up with are different (better) than those in post #1--why? The answer to this goes hand-in-hand with the next steps:

    Taking the information we came up with, it's time to make a drawing. From that drawing, we can make some first estimates of weight using statistical equations from Raymer or Gudmundsson or others. For various reasons, you may come out overweight. For example, in my case, the +6/-3 thing pumps up the weight a bit. I've also been fairly conservative (overestimating) the weight of a few components--at least I hope so!

    The effect of this is to change the "a" factor (see post #11).

    [​IMG]

    So now we get to start over with a new "a" factor. But Raymer provides a spreadsheet with his book that automates this, so you can rather quickly run through a lot of scenarios without all the tedious math. (I do think it's important to have a working knowledge of what the equations are doing "manually" before diving into the spreadsheet in order to avoid garbage in, garbage out). If you want to get more sophisticated, you can also have worksheets in your spreadsheet to calculate weight, moments, and wetted area, all of which you can feed into the main spreadsheet. Remember that as you do a checks on stability, you may be moving and/or resizing flying surfaces, and this too will trigger the need to run everything again. It can take many, many tries until everything begins to fall into place.

    So, the reason why the numbers are different is that this project has been through many iterations, and now the numbers are beginning to approach the way this plane will perform, rather than statistical averages. This is a big part of the reason why I've begun to focus on the structure. There isn't really much statistical data available on component weights for wood wings, tails, and fuselages, and most of the data I've used so far is for aluminum planes. Therefore, one of the next big exercises for me will be to work up a rudimentary structural design to re-check weight.

    That's enough of Raymer for now, since we have the basic sizing out of the way.
     

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  14. Dec 7, 2017 #14

    mcrae0104

    mcrae0104

    mcrae0104

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    I have been doing some CG & stability analysis the last few days. It seems likely that the fuel and baggage will be forward, as originally suspected. Some possibility of an aft aux tank is still under consideration for extended range. Got a little bored with the math for the moment and decided to slather some more joint compound over the cowling, which has just been modeling clay until now. I enjoy the crudeness of the process of smearing on this "cake icing" and then reducing it to a refined shape, all while the precise math is happening in the background.

    IMG_6103.jpg IMG_6099.jpg
     
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