Laminar flow P-51 Mustang wing analysis

So, back 40 years ago, I approached the local aircraft expert flyer/designer/builder about building a wing for my modified Volvo 1800. He didn't hesitate and wiped out his NACA pocket book of wing profiles and said I needed a P-51 Mustang laminar flow profile. I believed him, so fast forward, I still want to build it. Has anyone done an analysis of this wing? I don't have a lot of hp, so can't dedicate any power to drag. This is a non sanctioned street legal car built for mountain canyon carving. My three week search for any information turns up nothing and I am too math illiterate to do any calculations.

What's the dimensions of the CAD wing you've drawn up?

There should be data for the NACA 63-412 in "Theory of Wing Sections"... but I'm separated from my personal copy at the moment.

edit:   
in looking for things, realized it's endplate-mounted.  Side-view was throwing me off.

At this moment in time it is 54"x24".

After reading about pedestal mounting airflow interference and not wanting to build a swan neck mount, I thought that side mounts would be best. And the most outrageous looking. :)

VolvoHeretic said:

After reading about pedestal mounting airflow interference and not wanting to build a swan neck mount, I thought that side mounts would be best. And the most outrageous looking. :)

Yeah, pedestal mounting a Laminar wing section kinda defeats the purpose of choosing a laminar profile.  Endplate mounting has additional benefits, too.

Trying to fine tune my wing mounting design, I am moving the pedestals to the outside of the winglets and pivoting them at the wing so that there is little forward/aft movement.

The wing is 2-11/16" thick and I really like the idea of hot wire shaping 2 glued together pieces of extruded polystyrene with the glued seam along the cord line and then fiber glassing the outside. I want to insert a 2" piece of aluminum electrical conduit lengthwise at the new pivot points and weld that to (2) aluminum wing shaped endplates.

I used to build houses out of SIPS (Structural Insulated Panels) which consisted of chunks of 4'x8'x5.5" polystyrene bead board sandwiched/glued to (2) sheets of OSB panels. They never quite fit perfectly and you had to free form-hand fit/carve the insulation with a hot wire gun. 

And, I used to work at a fiberglass shop for a short while which came in handy when I built a Styrofoam/plaster of paris/fiberglass positive mold for the fiberglass negative mold for a fiberglass bodied 1/5 scale chainsaw powered remote control car I never built. :)

VolvoHeretic said:

This reminds me a bit of something...

Can't help with the engineering, but I am looking forward to seeing where this goes when the smart people get here.

lol Keith, that's funny. Who knew 40 years ago that a photo taken on the side of a cliff above Boulder, CO with an instamatic camera would come in handy. :)

I finished the car in San Diego in 1980 and then drove back home, next to the exact center of North America. I must hold some sort of record for that drive. I usually drove 90 mph when I wasn't working in-route on that thing's fuel injection system. ((accidently left in before welding) melted 16 gallon keg nylon plug contaminated gas tank).  :)

And, I see that I could have calculated the vanishing points and drawn the wing in perspective to the photo. I will get right on that...

I only have 140 hp and 160 lb-ft, plenty enough for 1978, but any kid in their Honda or my wife in her minivan could kick my ass. A little exhaust port work and a milled block and hot cam would yield 160 hp, and (2) stock turbos in the trunk with the stock 8.7:1 block would easily get 300hp with the cast crank. Why the redline of the 6 cylinder is only 6000 rpm and the rougher 4 banger is 6500 rpm is beyond me. I think it wouldn't matter as far as the valves where concerned. It scares the crap out of me as is and nobody on Broadway want's to race me from any street light. lol

What speed do you want this thing to work best? There might be a better airfoil to use than a P-51's.

VolvoHeretic said:

Trying to fine tune my wing mounting design, I am moving the pedestals to the outside of the winglets and pivoting them at the wing so that there is little forward/aft movement.

The wing is 2-11/16" thick and I really like the idea of hot wire shaping 2 glued together pieces of extruded polystyrene with the glued seam along the cord line and then fiber glassing the outside. I want to insert a 2" piece of aluminum electrical conduit lengthwise at the new pivot points and weld that to (2) aluminum wing shaped endplates.

I used to build houses out of SIPS (Structural Insulated Panels) which consisted of chunks of 4'x8'x5.5" polystyrene bead board sandwiched/glued to (2) sheets of OSB panels. They never quite fit perfectly and you had to free form-hand fit/carve the insulation with a hot wire gun. 

Could I interest you in doing an external mold?  It'll get a much better, and more even surface than an internal mold.  The hot wire is a great idea for this as well.

Look for my post on 11/3/20 on this page for a rough how-to 

Appleseed said:

What speed do you want this thing to work best? There might be a better airfoil to use than a P-51's.

I don't know, between 70 and 100 mph? There sure could be better airfoils out there, but I'm stuck in the 1960's/70's and Jim Hall's Chaparrals. This is my first serious attempt at thinking about building one.

I have re-united with my Theory of Wing Sections.  But, first, a caveat and a request.

Caveat:   
The following numbers are 'rough', and have some built-in assumptions, some of which might be wrong/off.  Hopefully not enough to where the information is errant.

Request:   
one of the short-cuts I've used is based around front/rear weight bias, and overhang lengths as a percentage... based on published wheelbase and 'over all length' dimensions.  I'm guessing it has a 55% weight on the nose, and that distance fro the front wheel centerline to the front bumper is 40% and the rear overhang is 60%.  But, if you gave me raw dimensions in inches of the following orange lengths, I'll update my calculations...

so, another couple of caveats...

I've done this initial 'napkin analysis' at 60mph; which I think should be fine for right now... it'll mostly mean that the 'raw downforce (in pounds)' values will look "low".  The main reason I'm providing them, is they help to show how I'm attempting to balance the aero load on the car.

I managed to find some basic numbers on the P1800, including 'Ax' cross-sectional area, and drag coefficient.  I reckon both of these are low, compared to your car... but it's a start.  I've also given a 'book-end' of 'low front downforce' and 'high front downforce' based on cross-sectional area; specifically 0.25 and 0.4;  which works out to ~43#s and ~70#s of downforce.

plugging all those assumptions (orange cells)... plus some values from ToW... into some equations/cells (blue cells)... we get the following:

so... !yay!... numbers!   but, what's it all mean!?

There's two main 'beneficial' take-aways from the wing you've designed:
1) The 24" chord means that even at a lowly 60mph, you're wing is up into the "normal Reynold's Number (Re)" regime.
2) The N63-412 in that wing (based on my assumptions), should be able to balance out the most front downforce I'd expect you to generate; but probably not much more.

Those two benefits, though, are weighed down by a whole bunch of detriments:
1) The 54"x24" wing means it has a planform AspectRatio (AR) of just over '2'  (2.25)... it's hard to tell how effective your pedestal mounts will be as 'end plates', so I've estimated them as having an 'aerodynamic effective height' of 8inches, which helps to bump the effective AR to 2.88.  Most of the time, anything under '5' is "low"... and anything under '3' is usually powered by a jet engine, or strapped to an F1 car.

2) The Low AR means the wing will struggle to make downforce, and it will have more drag that you'd like.

3) Despite an apparent 'excess' of area, even at the "Low Front Downforce" balance setting... the rear wing would need to be around 3deg and making a Cl of 0.7... which actually pushes the N63-412 'on the edge' to 'outside' of it's Laminar Drag Bucket... so you wouldn't particularly be benefiting from the foil's "claim to fame".

4) This is more a caveat.  But the drag coefficient I've included here is based on the 'wind tunnel test data' provided in Theory of Wing Sections, at 3e6 Re (about 3x what your wing would see); and I'm using the "perfectly clean test article" drag coefficient, not the 'standard roughness' coefficients... so the drag shown is probably a bit "optimistic" (i.e. low).  That's not a big deal now... but it's worth bearing in mind as I add more in.

I should have probably mentioned this elsewhere... but I think you have the wing mounted too low... and it'll block your rearward vision in "an annoying way"... while also creating an in-flow angle of attack (AoA) which might make it difficult to get the wing set right to balance the front.

Alright, TL;DR  / Summary:
I think the chord of your wing is too big.
I don't think the N63-412 foil is a good match for what you're doing.  It's fairly limited in camber, and the laminar drag bucket reduction falls outside of where you'd most likely end up attempting to use the wing/foil.

I think those are the main take-aways, from a 'napkin analysis' of that wing.  Next, I'll see about what a "quick, dirty, and cheap" alternative would look like / compare.

so, the "Quick, Dirty, and Cheap" option...

this is definitely not a laminar section (because a couple of reasons).  But, there's no foil to build... just order up an appropriate section*, and figure out how to mount it up in a way that lets you adjust the angle some.  Conveniently, they're a forum supporter; and you can also buy their sections from FlyinMiata.

$400 gets you a 9Lives Racing Build Your Own Wang... section?  thing?  which is technically 1" too long.  but... we'll get there...

I should probably make a paragraph of caveats here:  I've taken the data they've published in the past, which isn't exactly useful here "out of the box".  The published data is for a pedestal mounted wing that's 70" in span, and has (iirc) 8" deep endplates mounted to it.  I'm figuring on an end-plate mounted wing that's 54" in span.  So, in the background, I've done some... numerical regression?... numerical analysis?... numeri----.... I've hacked at their published data pretty hard to try and back out what an equivalent "2d" lift/drag coefficients would be for the 9LR/Morlind/Elan foil section.  I'm doing this so that I can apply it to a different span wing, and then compare it to the published wind tunnel data for the N.A.C.A. 63-412.  There's a definite possibility that I'm off by a factor of '2'.  If so, I apologize;  I don't have coordinates for the 9LR wing or the wing as it comes out of the extrusion... so I'm relying on their '3D' data, and some of the compensations I can think to apply.  The main benefit of taking this approach is: speed.  I can make these calculations/adjustments faster than you can set up a 3D model (let along run it).

so, plug all that into the same cells/formulae...

Here's where that astrix from above comes in.  One issue with a 54" 9LR wing, is that you'll probably fall short of balancing out the maximum front downforce.  Which, honestly from my view isn't a big deal.  looking at how the P1800's fins *seem* to angle out... and my suggestion that you push the wing height up... I'm going to guess that a 60" wing isn't "impossible" to make work (physically and visually)....

Going to a 60" span helps push the AspectRatio up over 7.  And, despite the 2d foil-section drag coefficient being ~4x that of the N63-412; the "installed 3D wing drag" is "about half" that of the 54"x24" wing... mainly due to reduced wetted area; but also because of the increased AspectRatio.

so, if you just want to run out and get a wing put on the back of your car;  and go and do that "right frelling now".  Then... 100%... the 9LR is definitely the way to go.  It's proven, it can handle the loads you'd throw at it (even end-plate mounted {afaik; especially if you use all 4 bolt-mounting points in the extrusion}), and the only work to do is fabbing up the mounts.

Now, if you want a "Laminar Flow Section, just like a P-51"... well, the answer to that one might take a couple additional days from me.

Wow sleepyhead the buffalo, Thanks a million for all the hard work. Ok, I didn't notice that I wouldn't be able to see out the back window, I spend so much time zoomed into the details that I can't see the big picture lol. Here are the dimensions of the car you where looking for. 60" wide would be fine, the rear flares are 6" on each side, so the car is 12" wider than stock (67" + 12" = about 79" wide). I will punt small children and animals out of the way with the flares before I decapitate them. The chord width was just something I pulled out of thin air, it could be less. I also made the endplates deeper. I will look at the 9LR because after watching youtube videos about diy carbon fiber wings, building my own will take me 10 years. :)

Is there a wing profile for the 9LR wing? (Edit:) It looks like this wing needs a Gurney flap to finish the profile, which doesn't make sense to me for the lowest drag possibilities. Shouldn't there be a way to extend the back to a nice sharp edge? Maybe some hard rubber glued on so it doesn't slice your next if you brush up against it?

VolvoHeretic said:

Is there a wing profile for the 9LR wing?

afaik, there's not public coordinates for it.  the best you can probably do is this, and then attempting to spline the outline into CAD.  The aluminum section in generally listed as 10.5inches in chord; although I've also seen references to it measuring out as 9.25inches... which could be down to differences in how people decide to measure the chord.

Thanks sleepyhead the buffalo.

VolvoHeretic said:

 (Edit:) It looks like this wing needs a Gurney flap to finish the profile, which doesn't make sense to me for the lowest drag possibilities. Shouldn't there be a way to extend the back to a nice sharp edge? Maybe some hard rubber glued on so it doesn't slice your next if you brush up against it?

It's has a built-in channel for variable gurney flaps; which they also extrude/sell.  It's not required to have them, to get the performance I posted above (and I avoided included them, since drag was a concern of yours).

could you trim the wing?  Definitely.  It's just aluminum... so it should 'work' on most 'wood working power tools'.
The most beneficial mod (in your case), probably, would be to trim it just ahead of the gurney section on a band-saw, with the foil 'low pressure side up'.  There'd probably be a benefit to subtly working the aft upper surface contour after doing that... but that'd probably take some considerably heftier analysis than I've performed thus-far.

edit after re-read:
the open gurney slot is so/so from a drag/performance perspective.  You could just tape it over with electrical tape or vinyl wrap if it bothers you.  There's nothing sharp about the rear edge of the 9LR wing, so no need to worry about it scraping you.

Lol, I just measured that blunt edge in my drawing and it is only about 3/16". The CFD analysis of the wing doesn't show any anomalies so I will round it off or at least dull it. My laminar flow wing would have been ground to a knife edge. I have never had a working speedometer, so all of my recollections are based off of the tack with long math done on the back of a 2x6, so very suspect. I know that I must have lost 10 to 15 mph top speed after sticking the new wheels, tires, flares, skirts and dam, I can't afford to loose much more. :) Do people actually use this wing at this pitch or is it just shown at 0 deg camber? I might have a problem finding a place with a water jet to cut out the pedestal pieces out here in the boonies.

After drawing a 3D model, I see a few issues with the pedestal. I didn't need to flare it larger at the top and I don't have any way of plotting out the curves on a flat sheet of aluminum so that after bending the angles, they all flow smoothly in side profile. I also question if it is even possible to bend the uprights accurately enough to make everything fit, maybe it would be better to cut and weld everything together? I am working at making the uprights straight after it clears the rear bodywork.

So, now what thickness aluminum sheet should I use? I have drawn it out of 3/8" 6061 T6 and it would be something like 3 or 4" deep. How about 1/4"?

Also, how much pitch adjustment should the wing have, every 5 degrees, 2.5 degrees?