Some More Model Plane Math!

While making a design for a flying wing recently, I came across some interesting things that can be very useful when designing an RC plane.

Lift Equation 

Lift = 0.5 * Wing area (in square feet) * speed squared (in feet per second) * air density * lift coefficient of the airfoil

If the number for lift is equal to the weight of the plane in pounds, it will fly. For example, say I have an aerobatic 3D RC plane with a symmetrical airfoil that has a lift coefficient of 0.5, a wing area of 5.5 square feet, and a total weight of 3 pounds. We think it should be able  to fly at a speed of 25 feet per second (27 kilometres per hour).

An example of a 3D (aerobatic sport) RC plane. 

Lift = 0.5 * Wing area * Speed squared * Air density * Lift coefficient       

       = 0.5 * 5.5 * (25 ft per second * 25 ft per second) * 0.0027 * 0.5
       = 0.5 * 5.5 * 625 * 0.0027 * 0.5
       = 4.64 pounds 

Because the lift generated by the wing (4.64 pounds) is more than the weight (3 pounds), assuming that the centre of gravity and everything else was correct, the RC plane would fly. The great thing about the lift equation is that not only can you find out if the lift generated by the plane is enough to overcome the weight at a given speed, you can also find the minimum speed that the plane would take off at (the point where the lift is equal to the weight). Let's go back to that example.

Lift = 0.5 * Wing area * Speed squared * Air density * Lift coefficient
       = 0.5 * 5.5 * (21 ft per second  * 21 ft per second) * 0.0027 * 0.5
       =  0.5 * 5.5 * 441 * 0.0027 * 0.5
       = 3.27 pounds 

We eventually find that the RC plane would need to be moving at a minimum of just under 21 feet per second (23 km/h) to takeoff, (remembering that we had 3.27 pounds of lift and the weight of the plane was 3 pounds).