Static Thrust Calculation
Calculations of static thrust are needed in order to ensure that the proper propellers and motors have been selected. Static thrust is defined as the amount of thrust produced by a propeller which is located stationary to the earth. This calculation is particularly important for this project because quadrotor helicopters are more likely to perform at low speeds relative to the earth. This low-speed performance ensures that the calculations of static thrust can be applied to a wide range of flight conditions. Also, it is important to note that the final calculations of static thrust are estimates and not actual values.
The first step in calculating static thrust is determining the power transmitted by the motors to the propellers in terms of rpm. Aircraft-world.com has compiled empirical data used to calculate power , and the formula used for their datasheet is given in Equation 1.
Where power is in watts and rpm is in thousands. For example, a 6X4 APC propeller has a propeller constant of 0.015 and a power factor of 3.2. Given a rotational speed of 10,000 rpm, the calculation goes as follows: Power=0.015X103.2=24 W.
The next step is to determine the thrust produced by a propeller. Equation 2 gives thrust based on the Momentum Theory.
A commonly used rule is that velocity of the air at the propeller is v=½Δv of the total change in air velocity: Therefore, and equation 3 is derived.
Equation 4 gives the power that is absorbed by the propeller from the motor. Equation 5 shows the result of solving equation 4 for Δv and substituting it into equation 3. In doing so, Δv is eliminated and torque can be calculated.
Finally, it is advantageous to express the results of equation 5 in terms of mass. Newton’s Law, F=ma, is used to obtain equation 6.
Solving for mass is useful for quadrotor helicopters because it can be directly related to the mass of the aircraft. In particular, a thrust (mass) that equals the mass of the aircraft is needed for hovering. The importance of hovering will be addressed in the following section (DC Motors).