CAR-251: The Cheap Air Racer Discussion thread.

Discussion in 'Hangar Flying' started by nerobro, Sep 10, 2014.

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  1. Sep 23, 2014 #221

    nerobro

    nerobro

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    My brain slipped on the whole "digging a bigger hole in the air" thing. So.. to simulate G loading, when doing the lift equation, I started plugging in higher weights.

    So, the plane ends up going a LOT faster. The highest g turn shows up between 80 and 90 knots, and about 1.6g.

    Watch Nero learn... :)
     
    Last edited: Sep 23, 2014
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  2. Sep 23, 2014 #222

    Autodidact

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    I assume you increased the weight in the SS to simulate the higher g? That sounds like it should work. BUT, did you factor in the Coriolis effect? :hammer: :D Just kidding.
     
  3. Sep 23, 2014 #223

    nerobro

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    I did. The stall speed goes up to something like 70kts. I'd need to look again.
     
  4. Sep 23, 2014 #224

    Autodidact

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    51° sustained turn is pretty good, considering it will take a little time to bleed off the speed.
     
  5. Sep 23, 2014 #225

    Matt G.

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    How did you get all the way down to ~10lbs of spar weight from the nearly 50 lbs I estimated for your previous design? Also, what are you using specific gravity for? Wouldn't it be easier to determine the structural weights with the density instead, or are you converting specific gravity to density?
     
  6. Sep 23, 2014 #226

    nerobro

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    I'm converting specific gravity to density. It's what I had handy.

    The spar is 8', it's (currently) 3" wide, and 6.3" tall. It tapers down to 3" at it's ends, and the center 2' are straight section. sometime soon i'll do some calculating to see if my "shells" for the outer 5' will cut the musterd.
     
  7. Sep 23, 2014 #227

    Victor Bravo

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    I almost hate to do this, but duty, honor, and country demand it.

    Roscoe Turner, the patron saint of air racing, appeared to me in a brief but vivid ethereal vision, resplendent in a light blue uniform that featured impossibly oversized golden pilot wings on his chest, beaming a big smile from under his pencil moustache, and holding a small playful lion cub in his hands.

    The Colonel put his hand out, to adjust the hard-earned Junior Birdmen of America wings on my lapel as he spoke, and with great bombast and pomp he said that I must deliver all of you a message... sent down from the towering cumulus clouds in the skies above him, which were shaped like thousand foot tall checkered pylons.

    In a staccato, clipped, hyper-dramatized voice that can only exist in Movietone Newsreels long since passed into history, he spoke these words to me...

    "In my day, son, we were forced to use wood, and castor oil, and glue our planes together using glue made from horse hooves. We only had ten-twenty mild steel tubes and used coat hangers as welding rods. It's all we had, so we had to make the structures much more complicated with a lot more parts, to keep them light...

    "But today you have something we never had, and that we would have given the clothes off our back for. Those little black strips of what you call pulltruded carbon fiber make a huge improvement in strength, they save an incredible amount of weight, and they're much easier and safer to use than the previous rolls of carbon yarn. They'll make today's racer safer, stronger, lighter, and faster....

    "But the thing that nobody seems to understand is that they're also incredibly cheap for the amount of strength they provide. A racing wing that has to be built for six times the force of gravity, and still be light enough to fly with a small engine, can actually be built cheaper by using these blacks trips than it could be built without them. A material analysis of strength versus cost shows that easily. The strips are so strong that you actually spend a little less of them than you would spend in wood or metal materials. A guy named Marske over in Ohio figured that out years ago.....

    "For goodness sakes kid, me and Wittman and Benny Howard and Jimmy Wedell... all the way up in the clouds we hear you and your friends in that darned invisible electric meeting room of yours arguing and babbling and coming up with all sorts of ideas about racing. Now you finally decide that you want to do it cheap! Look here kid, me and the boys were building racing airplanes in the Depression! We'll tell you all about having to be cheap! The loan sharks and mobsters were one step behind me at every turn back then. If we could have made an airplane faster, safer, stronger, and cheaper at the same time using some newfangled stuff you just glued on to your spars and longerons, we would have killed to have that stuff !". If you're willing to use better glue than we had, and better steel tube, and better engine oil, then why the hell are you not using this black magic stuff in a wing spar if it's strong AND cheap ?"

    And with that, the great Roscoe Turner disappeared in a fast-paced flurry of newsreel music, although I could swear I briefly heard the sound of an over-revved Wasp racing motor echoing once in the clouds for just a moment.
     
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  8. Sep 23, 2014 #228

    autoreply

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    And to get away from the "one guy with his pushrods", it's used in several aircraft, notably the certified Lak17/19. Impressively light wings, even compared to conventional carbon spars.
     
  9. Sep 25, 2014 #229

    BJC

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    $30,000 total airplane kit, 600 pound empty weight, designed to be easily transported, +6 / -3 g, with a turbo VW option (more $'s) that would enhance performance at Reno. Over 20 completed and flown.

    Sonex -- The Sport Aircraft Reality Check!
     
  10. Sep 26, 2014 #230

    nerobro

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    I viewed the graphical method as cheating. I could do that tonight.. instead of continuing to try to re-teach myself the math...
     
  11. Sep 26, 2014 #231

    Autodidact

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    Here, read this NACA report (NACA-TR-572), too. It is as easy as graphical Schrenk's method, and provides much more information such as moment coefficient spanwise distribution (and of the wing as a whole), A.C. of the wing (as opposed to just the airfoil section), and also has a way to estimate the maximum lift coefficient of the wing where stalling begins, and is (reasonably) accurate for wings with as much as 30° sweep (one example, with 15° sweep, looks just like yours). It's also very easy, with simple math, and charts and graphs:

    NASA Technical Reports Server (NTRS) - Determination of the characteristics of tapered wings
     
  12. Sep 26, 2014 #232

    nerobro

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    Thank you!
     
  13. Sep 26, 2014 #233

    Hot Wings

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    There is also the Schrenk original report NACA TM-948 that can be found at the link above.
     
  14. Oct 1, 2014 #234

    nerobro

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    [​IMG]

    Hello lift distribution graph.

    If we count the area of the wing "inside the fuselage" 8' of span covers 63% of the lift the wings generate. (this makes flaps on just the center section of a wing make a whole heck of a lot more sense... and why you don't see drooping alerions very often.)

    Since the wing changes structure at the 3' out into each wing panel, and the wings essentially become monocoque at that point.. I have my work cut out for me math wise. At least with the lift distribution I can do math on the wing root with some confidence.

    Edit: So how did I come up with the lift distrubution graph?

    I used a circle. I chose one that was 18 units across. Using an equation to find the area of the "curve" bit of a slice of the circle, I found area at 8.5, 8, 7.5, etc.. so I got 18 slices on one half of the circle. If I understand the equations right, this would give me the right shape of the curve. The height of the curve, would be modified by how much lift the wing was generating.

    Now my wing is tapered, so the curve needed to be modified for the wing area at each station. I multiplied the straight results by the mean chord for the inboard side of each station. So instead of assuming a multiplier of 1, as if the wing were straight, I started at a multiplier of 1.563, and ended up at 3.483 at the wing root. That took the curve from an ellipse, to the thing you see above.

    The numbers I had at that point, were "not tied to anything but geometry" so I added them up, to get the total area under the curve. I then went to each column and divided the calculated number by the total, so I would get a percent of lift at each station. And that's what the graph shows. It seems to match the graph for other tapered wing plans as well, so I am pretty pleased with what I came up with.

    Now we get to go back to the 11,000 pound number, and I get to divide that across all the stations. This should give me a much better idea of the bending moment on the wing root.

    I also have a bit of a question. When calculating wing loading, and moments, do you ignore the are in the fuselage? or count the fuselage as lifting surface? re-calculating for either isn't hard in this case. Not counting the fuselage is definitely the safer choice...
     
    Last edited: Oct 1, 2014
  15. Oct 1, 2014 #235

    Autodidact

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    Nerobro, I'm not trying to hassle you, but from the looks of your graph, and from your description of the process you used, I don't think you got the correct lift distribution. The units across isn't the important thing for the circle/ellipse, it's the area that is important; it has to have the same area as the wing area. You superimpose the ellipse over the drawn wing, slice them up, measure the two heights for each slice (wing & ellipse), then add them together and divide by two to get the average height of the slice . Now find the area of the slice (up to the average height) , and divide that by the total (semi-span) wing area, and that gives you a percentage or coefficient by which to multiply the total lift on that wing panel (depending on the g-loading) to find the lift on that slice of the wing.

    The lift distribution you've drawn is almost a straight sided triangle, and that almost never happens and when it does, it's because there is a lot of twist (washout) in the wing. Not to mention that you've got the entire span drawn (18 ft, right?) as if it were the half-span.

    Here,

    [​IMG]
     
    Last edited: Oct 1, 2014
  16. Oct 1, 2014 #236

    nerobro

    nerobro

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    I got it wrong, but not by as much as I think you think. My tapered wing modifier is well and truly off. I need to re-think how I did that.

    An oval is just a stretched circle. By using a circle to generate the ratios of area, I think I still come out with the right curve. For a constant chord wing at least.

    How I'm compensating for the tapered wing.. I need to question.
     
  17. Oct 1, 2014 #237

    Matt G.

    Matt G.

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    How does one mathematically 'stretch' a circle? A circle is a special case of an ellipse where the lengths of the major and minor axes are equal. You can use the equation of an ellipse to draw a circle, and find the areas of the segments, but I don't understand how you're doing this the other way around by using a circle to come up with the strip areas for an ellipse.

    What reference are you using for the calculation? Schrenk's paper, Hiscocks's book, or something else?
     
  18. Oct 1, 2014 #238

    Autodidact

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    You don't have to calculate the lift distribution for the entire wing, only for half of the wing, since it is symmetrical. And you can use a circle IF you follow this procedure: slice any 1/4 circle (it doesn't matter what radius) into the same number of slices as the wing semi-span. Find the area of a slice of the 1/4 circle and divide that by the total area of the 1/4 circle (regardless of what that area is, it's the ratio that's important...). Now find the area of the corresponding slice of the wing semi-span and divide that by the total area of the wing semi-span. Add the two ratios and divide by 2 to get their average.
     
  19. Oct 2, 2014 #239

    Matt G.

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    Well, after about 3 hours modifying my spreadsheet for spanwise load distribution from Hiscocks' book (well, half an hour of modifying it and 2.5 to discover the missing square root in one column), I managed to determine that the answer will come out the same with an ellipse or circle.

    Based on that, I should be able to put Nerobro's taper ratio (0.4 measured from his sketch) Max gross weight (500 lbs) and wing half-span (I'll also incorrectly use 18 ft to try to match his graph) into my spreadsheet and get the same answer for 1g loading. I don't.
    SpanwiseLoad.jpg

    Note: X-axis label BL = Butt Line = lateral distance from aircraft centerline.

    The shape of the curve is different, as are the values. I'll also note that while there could still be an error in my spreadsheet, I was able to reproduce the example in Hiscocks' book with it.


    Nerobro, I think the problem with your trapezoidal area is that you didn't use an area for it equal to the area of the quarter-circle. If you non-dimensionalize the circle by giving it an area of 1, then the trapezoidal area must also have an area of 1. To do this, make the length equal to the radius of the circle, and the root and tip heights such that the ratio of tip height to root height is the same as your wing's tip chord divided by root chord. Thus, the taper ratio of the trapezoid must be the same as the taper ratio of your wing, and the area of the quarter circle (or ellipse) must be the same as the area of the trapezoid. If you make the areas of those equal to one, you can average them and multiply by the amount of load that one half of the wing carries. This is the way it is done in Hiscocks' book. The advantage to the ellipse is that you can make the semi-minor axis equal to 1, and use a trapezoid with a length of 1. With a circle, you get some nastier numbers if you want loads at each 10% of half-span. Confused yet?:lick:

    Hopefully some of this made sense. It is getting too late in the day for me to be able to write coherent sentences...
     
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  20. Oct 2, 2014 #240

    Autodidact

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    I never thought of that; as long as the taper ratio is the same, and the number of slices is the same, you always get the same (area-of-slice)/(area-of-trapezoid) ratio. Same with an ellipse: you can take a 1/4 circle sliced into "n" slices, extend its horizontal axis by 2 or 3 (or whatever) times while keeping the same number of slices, and get 2 or 3 times the area and since the slices also increase in width by the same factor, you get the same slice/area ratio regardless of the areas.

    If Nerobro's not confused by now, I don't know what else we can do...;)
     

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