By Bruce Carmichael, 34795 Camino Capistrano, Capistrano Beach, CA 92624; CONTACT Magazine, Vol 5, Number 1, Jan - Feb 1994, Issue 24
The AR-5 is a composite construction, low wing, fixed gear, tractor monoplane powered by a liquid cooled 65 horsepower Rotax 582 engine. The fact that this configuration, which had not been designed as an all-out racer, had captured the world speed record for take-off weight of 661 pounds or under, makes it highly interesting for drag estimation study.
AERODYNAMIC ASSESSMENT:
At Mike's invitation, I first visited his shop for a detailed inspection of the AR-5, including checking the wing for surface waviness with a wave gauge. The workmanship is superb and a look at it in glancing light makes a wave gauge reading almost superfluous. It was no surprise when the largest wave I could find over the spar area was 1/1000 ratio of wave height to wave length. The external aerodynamic drag estimates need no corrections for surface roughness. The surfaces are remarkably free of protuberances and all joints and control surface hinge lines are beautifully executed. The internal aerodynamics of the cooling system leave room perhaps for some additional refinement. Since I did not have enough detailed internal geometry, this report calculate only the external drag and then inquires as to the margin from the total drag (calculated from speed, power, and assumed propeller efficiency) left over for cooling drag. I did not used the record speed of 213 mph for the analysis but rather Mike's best estimate of his maximum level flight speed of 207 mph. The record setting rules permit an assist from gravity to enter the course a bit above maximum level flight speed.
WING DRAG:
The aspect ratio eight, 55.125 square foot, low drag wing has a taper ratio of 0.78, a NACA 65/3-418 root airfoil, a NACA 65/2-215 tip airfoil, 50 percent span, 25 percent chord, flaps, and 44 percent span, 23 percent chord ailerons. The wing area exposed outside the fuselage is 49.6 square feet, and its wetted area is 102.6 square feet. At 207 mph at sea level the Reynolds number per foot of length is 1.94 million. The average chord is 2.7 yielding a wing Reynolds number of 5.15 million. The low turbulence wind tunnel data (1) gives a profile drag coefficient of 0.0047 for the root and 0.0045 for the tip. The resulting drag area for the exposed wing is 0.228 square feet. The slight losses due to turbulent wedges at the tips, roots and landing gear intersections, plus the slight discontinuity at the flap and aileron hinge lines will probably raise the average profile drag coefficient to 0.005, giving an exposed wing drag area of 0.248 square feet. The wing loading is 12 pounds per square feet, the dynamic pressure is 109.6 psf, giving a lift coefficient of 0.109. The induced drag coefficient is 0.00053, or induced drag area of 0.029 square feet.
FUSELAGE DRAG:
The 14.5 foot long, 23 inch wide, 35 inch deep fuselage has a length to effective diameter ratio of 6 and a frontal area of 5 square feet. Mike figured the wetted area from the plans and I figured it from measurements that Mike, my son Doug, and I made during the inspection. I cross-checked to within 1/3 of one percent of Mike's figure of 83 square feet. The canopy is 19.1 inches wide and protrudes 9.55 inches above the forebody.
I shall initially assume the fuselage boundary layer is completely turbulent and that there is no roughness drag. The internal flow drag will be ignored for now and it is assumed that the inflow in flight is correct to avoid affecting the external flow at the nose. The basic wetted area drag coefficient is found on the streamlined body charts of Young (2) for transition at the nose ( length Reynolds number of 29 million, and length-to-effective-diameter ratio of 6), to be 0.0029. What must we increase this by to take into account the flat faced shape difference from a streamlined body?
It has been found (3) that Navy torpedoes with a flat face of half the body diameter, faired elliptically into the forebody, had the same drag as a streamlined body (of the same wetted area). Still, I will use a 5 percent increase, to acknowledge the shape difference.
The canopy has a raised frontal area of 0.99 square feet. Hoerner (4) gives a frontal area incremental drag coefficient of 0.04 for a clean canopy. Mike has faired his in at the front, thus softening the adverse pressure gradient on the fuselage approaching the canopy. If we use a coefficient of 0.03, we get an increment in drag area for the canopy of 0.0297 square feet. The fuselage as a glider would have a drag area of 0.0029 x 83 x 1.05 + 0.00297 = 0.827 square feet.
Now we must increase the drag to account for the propeller slipstream. Hoerner gives a value of 7 percent. More recent NASA work (5) indicated that slipstream effects on the mean behavior of the boundary layer are perhaps less drastic than originally assumed. We shall use a 5 percent increase until further data is available. The fuselage drag area in powered flight is therefore 0.297 square feet. The frontal area drag coefficient is 0.059, and the effective fuselage wetted area coefficient is 0.00358.
WING/BODY INTERFERENCE DRAG
Mike has not started contracting the fuselage until almost at the wing trailing edge which will help reduce the low wing intersection problem somewhat in the high speed condition, and especially at the higher lift coefficients in the climb. He has also provided a planform radius at the leading edge, which softens the adverse pressure gradient on the fuselage boundary layer as it approaches the wing stagnation. He has a small but adequate radius in the wing fuselage corner as seen in front view, which limits the pile up of boundary layer one finds in a right angle intersection. It is important to do as Mike has done and not overdo this radius, as that would increase the super velocities at the thick point of the wing and steepen the adverse pressure gradient to the rear. The lower surface of the wing is tangent to the lower fuselage, thus eliminating two corners.
Estimating intersection drag is a chancy business, unless one has the new, powerful computer programs as mentioned in John Rontz's fine article in the February 1991 Sport Aviation Magazine (6). In the past, it was set equal to the wing area enclosed within the fuselage, figured at the exposed-wing drag coefficient. On this basis, the 23 by 34.6 in area gives a drag area increment of 0.028 square feet for the intersection. This is 5 percent of the sum of the wing, alone, and body, alone, drag areas. Hoerner suggests a 4 percent increase for each juncture, at normal wing locations. Due to the beautiful filleting job Mike has done I will assume 3 percent for each juncture, or 6 percent of the sum of wing and body. This comes to an intersection drag area of 0.033 square feet, for the high speed condition.
TAIL SURFACE DRAG ESTIMATION:
The horizontal tail has 13.26 square feet of area, an average chord length of 1.75 feet, and a Reynolds number of 3.39 million. The 11 percent thick low drag section has a profile drag coefficient of 0.0042 (1) giving a horizontal tail drag area of 0.0557 square feet. The vertical tail has 7.35 square feet of area, an average chord of 2.5 feet and a Reynolds number of 4.8 million. The 10 percent thick, low drag section will have a profile drag coefficient of 0.0038 (1), giving a vertical tail drag area of 0.0836 square feet. This must be increased by 8.7 percent for hinge lines and each of the 6 junctures causes a 1 percent increase in drag in the tail location.
This is less than a wing juncture, according to a study in Hoerner (4) showing the variation in intersection drag with location along the fuselage. We must also account for the influence of the slipstream. If the tail surfaces were made completely turbulent by the slipstream, it could double the profile drag coefficients. Recent RASA studies (5) have indicated the time average effect may be considerably less severe. Until further data is in let us assume a 40 percent increase. The total tail drag area is, therefore, 0.0836 x 1.4 x 1.062 x 1.043 = 0.13 feet squared. Note that the hinge line and intersection increases as originally figured for laminar surfaces have been considered constant, are thus a lower percentage increase for the partially turbulent surfaces in the propeller slipstream.
LANDING GEAR DRAG ESTIMATION
The clean, fixed landing gear consists of two airfoil shaped leg fairings, 21 inches long, 1.38 inches thick, and 4.5 inches in chord. Thickness ratio is 0.307 and chord Reynolds number is 723,000. Frontal area of both is 0.403 square feet, and frontal area drag coefficient is 0.044 (7). Resulting drag area is 0.018 square feet. The 24.75 in long by 8.75 inch deep by 6 inch wide wheel pants, at a Reynolds number of 4 million, have a wetted area coefficient of 0.00465 square feet (2), if completely turbulent. This, times a wetted area of 6.8 square feet for both, gives a drag area of 0.032 feet square feet. The protruding wheel area is 0.11 square feet and, with a frontal area coefficient of 0.1 (4), yields a drag area increment of 0.0047 square feet.
The three inch diameter, 1.5 inch wide tailwheel has a frontal area of 0.032 square feet, and a Reynolds number of 500,000. Applying the drag coefficient of a supercritical sphere of 0.1, we get a drag area of 0.0032 square feet. Each landing gear leg has two intersection with the wing and one with the wheel pant, increasing the leg drag by three percent, which adds an increment of drag area of 0.0005 square feet. The total drag area of the landing gear is 0.0694 square feet, of which the legs give 26 percent, the pants 46 percent, their interference 1 percent, their protruding wheels 16 percent, tail wheel strut 6 percent, and tailwheel 5 percent. It would be interesting to put one main gear in a wind tunnel to see if the drag is as low as this calculation.
SUMMING UP
First, let's add up the incremental drag areas calculated thus far for the external aerodynamics. By subtracting this from the total effective drag area found from the top speed of 207 mph, we can see if anything is left for cooling or internal drag.
- Induced drag: 0.029 square feet ------(03.6 percent of total drag)
- Wing profile drag: 0.248 (30.8%)
- Fuselage drag: 0.297 (36.8%)
- Wing/body intf.: 0.033 (04.1%)
- Tail drag: 0.130 (16.1%)
- Landing gear drag: 0.069 (08.6%)
- Total external drag 0.806 square feet(100.00 percent)
As a glider, with the internal system sealed, the total drag area converts to a drag coefficient based on wing area of 0.0146.
It can also be converted to a wetted area coefficient of 0.0034 (by dividing by the total wetted area of 236.4 square feet.)
We can solve for the total effective drag area in flight by using the estimate of top level flight speed of 207 mph, brake horsepower of 65, and 82 percent propeller efficiency. This yields a drag area of 0.88 square feet. Subtracting our total external drag area of 0.806 square feet yields a difference of 0.074 square feet, or 8.4 percent of the total available for cooling drag. The drag breakdown is now:
Induced drag 0.029 square feet (03.3 percent of total drag)
Wing profile drag 0.248 (28.2%)
Fuselage drag 0.297 (33.7%)
Wing/body intf. 0.033 (03.8%)
Tail drag 0.130 (14.8%)
Landing gear drag 0.069 square feet (07.8%)
Cooling drag 0.074 (08.4%)
Total drag 0.880 (100.00 percent)
Total Drag Coefficient based on Wing Area = 0.016
Total Wetted Area Drag Coefficient = 0.0037
These final drag figures are quite remarkable for a low wing, fixed gear, tractor propeller, manned airplane. The drag area (which is a product for the size and cleanliness) of less than one square foot has not often been achieved. The wetted area coefficient of 0.0037 at a wing Reynolds number of only 5 million and a fuselage Reynolds number of 29 million, is remarkably low, and it includes all the increases from perfect streamlined body data, including the cooling drag. This cleanliness factor (0.0037) is lower than the lowest number published for propeller driven aircraft in the past of 0.0040 for the P-51 fighter. The P-51 flew at higher Reynolds numbers, had a fully retractable landing gear, and achieved zero cooling drag.
Many aerodynamicists will consider the coefficients of this study as optimistic, but sailplane designers might not, if they had the opportunity to examine the AR-5 as I did. Finally, even if the maximum level flight speed should be 200 mph, instead of 207, and if 72 instead of 65 hp were coaxed from the engine, the drag area would only be 1.12 square feet at 85 percent propeller efficiency, and the wetted area coefficient would be 0.0047. { I think it's more likely that the flight speed is correct, that engine horsepower is down around 60 or less, and that the propeller efficiency is no more than 82 percent. But, of course, I would think that, wouldn't I? M.A.}
The AR-5, and two recent Formula 1 raceplane designs, have demonstrated that quite high performances can be achieved with fixed landing gear, tractor propeller airplanes when laminarized through composite construction, together with great attention to detail design to eliminate all unnecessary sources of drag. While increased gains through laminarization can theoretically be achieved by pusher aircraft, and further reductions in wetted area can be achieved with retractable landing gear, it is not at all simple to beat the simpler configuration in practice. B.H.C.
REFERENCES
(1) Abbott, I.H., and Von Doenhof, A.E., "Theory of Wing Sections", Dover Publications, Inc N.Y. 1949
(2) Young, A.D., "The Calculation of Total and Skin Friction Drags of Bodies of Revolution at Zero Incidence", ARC R&M 1874, Apr 1939
(3) Phone call by writer to engineers at Naval Ordnance Test Station, Pasadena 1962
(4) Hoerner, S.F., "Fluid Dynamic Drag", Published by the author, Vancouver, WA 1958
(5) Holmes, B.J., Obara, C.J. and Yip, L.P., Natural Laminar Flow Experiments on Modern Airplane Surfaces" NASA Tech Paper 2256 June 1984
(6) Roncz, J., "Evolution of a Homebuilt Design", Sport Aviation Magazine Feb 1991
(7) Carmichael, B.H., "Two Dimensional Airfoil Literature Survey", North American Autonetics C6-1796/020 Aug 1996
Bruce H. Carmichael graduated with a degree in Aeronautical Engineering from the University of Michigan in 1944. Among his teachers was fellow EAA member Ed Lesher. Bruce later worked at Chance Vought and Goodyear Aircraft in applied aerodynamics. A chance meeting with Dr. August Respet at a sailplane meet in 1949 led to Bruce's joining him in boundary layer control flight research using sailplanes. This in turn led to extension of his research at high subsonic speeds with Dr. Werner Pfenninger at Northrop Aircraft, using an F-94A jet aircraft. He later extended both natural laminar flow and artificial boundary layer control for drag reduction with Dr. Max Kramer, using unmanned underwater vehicles.
He has served on aerodynamic committees for various soaring organizations, and written articles for soaring and aviation magazines. Retired in 1989, Bruce has had the good fortune during his career to return over and over again to the subject of drag reduction and vehicle transportation efficiency. M.C.M. CONTACT Magazine
