The Wright Brother's Wind Tunnel Balances
by Craig Hange
October 9, 1998
(This is an analysis of the Wright Brother's force measuring balance. It is aimed at grade 10 and up. An understanding of algebra and trigonometry is required to understand the derivation.)
As an engineer, one of the characteristics I've come to appreciate most about the Wright Brothers was their use of experimentation and analysis. Unlike many of their contemporaries, they did not just go out and build their airplane, and then try to fly it. They experimented with gliders, analyzed data, and even conducted a wind tunnel test before they flew in 1903.
Since I am involved with the test of the 1903 Wright Flyer to be conducted in the NASA Ames 40 X 80 wind tunnel next year, I found the fact the fact that Wilbur and Orville had conducted wind tunnel tests to be quite interesting. I was also motivated by an e-mail we received at the Aeroquest On-Line web-site where a teacher was inquiring about gaining some information about the wind tunnel balances the Wright Brothers had used. As I discovered more information, I learned that Wilbur and Orville had demonstrated their genius to this activity as well as their airplane.
For those of you who don't know, a device called a balance is used in a wind tunnel to measure the forces acting by the airflow on the model. We will be using an electronic balance when we test the Wright Flyer. Our balance is a high precision instrument, whose design has been refined in the last fifty years since the Wright 1903 flight. It also costs on the order of $30,000 to $50,000. The balances the Wright Brothers used however, were fairly simple devices, and although they were cheap to build, they gave good results, and provided Wilbur and Orville with the data needed to refine their airplane.
The 1901 glider had not performed as well as expected. The wings did not seem to generate as much lift as the data tables said they should. The brothers began to suspect the tables were in error. So in order to test new airfoils they se up an apparatus on the handlebars of a bicycle. This apparatus gave them good results, but it was very hard to conduct a good experiment while riding down the road on a moving bicycle.
So, in order to make their experiment more precise and repeatable, the Wright Brothers built a wind tunnel. It was made out of an old starch box, and a small fan blew the wind past the airfoils mounted to the Lift Balance or the Drift Balance.
In this particular write up we are going to be investigating the Drift Balance. Drift was a term that the Wright Brothers used for what we call drag. Through its mode of operation, the Drift Balance actually measures the ratio of drag-to-lift. This ratio is important, because the lift-to-drag ratio (the reciprocal of drag-to-lift) has a direct impact on how far a glider will fly, or minimize the amount of thrust (and therefore fuel) needed to keep a powered airplane in the air.
In the image above you see a symbol that looks like this is meant to be the Greek symbol Theta. It appears in the equations below as well.
Figure 2 shows a top view of the apparatus. Notice that the device is supported at P and Q to the floor, but arms C and D are free to pivot about those points. A pointer perpendicular to C indicates the angle of deflection, which is labeled in figure 2. Braces A and B are pinned to arms C and D so that the whole apparatus forms a parallelogram. When there is no wind blowing and the deflection angle is 0Á the parallelogram is a rectangle.
When the wind is blowing, the lift generated by the airfoil is transmitted through brace A, and it tries to turn arms C and D clockwise. The drag is also transmitted through A, and it tries to move C and D counter-clockwise. There is an angle where these two forces balance each other, and with that angle, it can be shown that tangent ( ) is the ratio of drag-to-lift.
Refer to the enlarged view in figure 2. In order for arm D to stop spinning and maintain a steady angle, the torque about its pivot point Q must add up to 0. The only forces contributing to the torque are the LIFT and the DRAG. There is also some force contributed by the airflow hitting the apparatus. The Wright Brothers assumed, and so will we, that this force is negligible, and contributes equally since the apparatus is symmetric to the airflow (with the exception of the airfoil). We now have enough information to form some equations. The sum of the torque acting at Q is 0.
DRAG*L1*cos( )+(-LIFT*L1*sin( ))=0
The torque caused by the drag is positive since it is trying to spin D clockwise, and the torque caused by the lift has a negative sign since it is trying to spin D clockwise.
Factor out L1 since it is in both terms
DRAG*cos( )+(-LIFT*sin( ))=0
The expression for the torque due to lift can now be moved to the other side of the equation by adding the opposite expression to both sides
DRAG*cos( )=LIFT*sin( )
Now divide both sides of the equation by the LIFT
(DRAG/LIFT)*cos( )=sin( )
Now divide both sides by cos ( )
(DRAG/LIFT)=(sin( )/cos( ))
And finally, make a trigonometric substitution
By measuring the angle off of the pointer with a protractor and using a reference book with the tangent function for various angles, the Wright Brothers could determine the drag-to-lift ratio for many airfoil shapes. They not only found a more suitable airfoil for their 1902 glider, but showed the data tables to be in error as well.
Reference: Jakab, Peter L. Visions of a Flying Machine - The Wright Brothers and the Process of Invention Shrewsbury England: Airlife Publishing Ltd., 1990