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Supersonic Wind Tunnel Testing For Performance of Next Generation Supersonic Transport

by Steve Smith

February 7, 2000

Over the past five years or so, NASA has been involved with Boeing Commercial Airplane Co. and McDonnell Douglas, Inc. (now part of Boeing), to develop the technologies to design a new supersonic transport. The Concorde jet is currently the world's only supersonic transport, and its operating costs are so high that it is not commercially viable. It is profitable only as a "luxury liner" with ticket prices too high for most people to be able to fly on it. If better aerodynamics could be combined with more efficient engines and lighter-weight structures, it may be possible to build a supersonic transport that would be profitable with ticket prices only slightly higher (maybe 10%) than current prices. In that case, many business travelers would be willing to pay the extra cost to reduce the time they spend traveling from the US to Europe and from the US to Asia.

One of the biggest challenges to building an economical supersonic transport is achieving low supersonic cruise drag. To study how well computer simulations can predict the supersonic cruise drag, a series of very careful wind tunnel tests were done on models that were also analyzed with computational fluid dynamics (CFD) simulations. These models were based on designs for a 300-passenger supersonic transport capable of flying from San Francisco to Hong Kong. To give you an idea of how important drag is for a supersonic transport, it was found that the added fuel needed to make up for a 0.5% (one-half percent!) error in drag prediction required the removal of 18 passengers to meet the same take-off weight limit.

Naturally then, it is really important to get accurate measurements of drag in the wind tunnel. The wind tunnel model itself is machined to very precise tolerances out of steel, and polished very smooth. The wind forces on the model, lift and drag, are measured with an electronic "balance" installed inside the model. The drag is defined as the force acting in a direction parallel to the wind, and the lift is defined as the force acting perpendicular to the wind. Since the balance is fixed to the model, the forces it measures are called "normal force" and "axial force" with respect to the model coordinate system. These body-axis forces are converted to wind-axis forces by measuring the angle of attack (the angle of the wind with respect to the model) with a very precise "tilt sensor." We try to measure the axial force to within 0.2%, the normal force to within 0.2%, and the angle of attack within 0.005 degrees. The errors in all three combine to give almost 0.5% accuracy in drag force.

Fun with Math!
Can you derive the equation to convert from body axis forces (normal force and axial force) to drag force?

D = A cos (alpha) + N sin (alpha) D=drag, A=axial force, N=normal force, alpha=angle of attack

Also, small errors (delta) in the measurements accumulate to form the error in the drag. Can you derive that equation by using chain-rule differentiation? Assume alpha is a small angle.

delta-D = (delta-A) + (delta-N)(alpha) + (N)(delta-alpha)

Designing a wind tunnel model for testing at supersonic speeds presents some special problems. One thing that happens at supersonic speeds is that shock waves form from the nose of the airplane, and from the wing leading edges. These shock waves spread to the side, similar to the bow waves from a ship. In flight, these waves extend all the way to the ground and make a sonic boom. The boom sound is how our ears react to the sudden pressure change as the shock wave sweeps past. In the wind tunnel, the shock waves bounce off the side walls of the wind tunnel. If they were to reflect back onto the model, they would create an unrealistic pressure pattern on the model. Since the goal of the test is to simulate free flight, the model size and location in the tunnel must be chosen so that the reflected shock waves do not hit the model.

The actual wind tunnel testing for drag is fairly simple. We try to hold test conditions very steady, including temperature. The electronic force balance can be very temperature sensitive. Ultimately, we even calibrated the balance at different temperatures so we could adjust the measurements for temperature variations. We take many measurements from each balance gage to average together to get the forces. We do several repeat runs to demonstrate the statistical repeatability of the data.

In addition to testing the basic design of the wing and body, different engine installations can have a big effect on the drag. Locating the engines carefully can cause favorable interference effects, where some of the drag on the engine is cancelled out by a reduction of drag on the wing in the presence of the engine. So many engine nacelle designs and positions can be studied. Another design feature that was tested was the leading and trailing edge flaps. Previous "test journals" by Mina Cappuccio and Fanny Zuniga describe some of those tests.

To give some idea of the kind of performance improvements that were achieved during the NASA-industry study, the Concorde jet has a lift-drag ratio of about 7.3 at Mach 2. The best designs from the recent NASA-industry study would have lift-drag ratios of about 9.0 at Mach 2.4.

 
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