# Desert Aerospace LLC

#### Last update 28 November 2015

Basic thrust equations:

#### Q: How much thrust does an aircraft need to fly?

A: The 'back of the envelope' calculation for this is simple. In flight, there are four opposing forces acting on an aircraft; lift, drag, weight and thrust. In straight and level flight, these forces are balanced (lift = weight and thrust = drag). Therefore, if we know the lift to drag ratio (L/D) of the aircraft, we also know the thrust to weight ratio. Divide the weight by the L/D to determine the minimum thrust required for level flight at best L/D speed. Example for BD-5:

Takeoff weight(W): 850 lbs

L/D: 15

Thrust required for level flight (at best L/D speed): Tmin = W/(L/D) 850/15 = 56.7 lbs (eq. 1)

To determine rate of climb (approximate), first subtract the thrust required for level flight (from equation 1) from the engine's maximum thrust rating. The remaining thrust is available to climb. The ratio of climb speed to forward speed is equal to the ratio of available thrust to weight. Assuming best L/D speed for the climb, we get the following for our BD-5 example above:

Engine total thrust(Ttot): 247 lbs

Thrust required for level flight (Tmin from eq. 1): 56.7

Best L/D speed(Vg): 120 knots

Available thrust: Tav = Ttot - Tmin 247 - 56.7 = 190.3 (eq. 2)

Ratio of weight to available thrust: W/Tav 850/190.3 = 4.47 (eq. 3)

Rate of climb (at best L/D speed) Vg/(w/Tav) 120/4.47 = 26.85 knots (2719 ft/min) (eq. 4)

Notes:

The aircraft's maximum speed is the speed where the aircraft drag equals the engine's maximum thrust.

Most efficient loiter speed is max L/D speed

Most efficient cruise speed is the speed where the L/D is 86% of max L/D

Don't forget to include the extra drag of the engine(s) in your calculations.

Most jet engines cannot maintain maximum thrust for extended periods. Their continuous thrust rating will be quite a bit lower than maximum. For example, the continuous thrust of the TJ-100 engine is about 70% of maximum.