# EDF Simplified Thrust Calculation?

So I am making my own EDFs that are 3D printed. The inside volume of the tube is 412,132 cubic millimeters I believe: Inner diameter is 80mm and length was 82mm

The hub diameter is: 40mm

Calculated FSA: 69.28

I’m using a standard 9v dc motor.

The calculated Kv for this motor is approximately 2,222

The calculation I found was:

Thrust = Mass flow rate * (Exhaust Velocity - Free Stream Velocity)

I went to calculate for mass flow rate as a start but that requires velocity and I can’t find a resource that tells me how to calculate for velocity without asking for mass flow rate which requires Velocity to calculate for 🤦‍♂️ .

Is that the velocity that the motor/fan spins at or is it the velocity that the air moves through the fan, or is it something else?

I know the density of the fluid is a part of that Velocity calculation and the Mass Flow Rate calculation. Given the fluid is just air I found that it’s 12.01 Pascals at sea level. I’m about 157ft above sea level.

I will then need to find Free Stream and Exhaust Velocity and I am not sure how to do that!

Can you give me an equation that gives me Thrust that uses any combination of only: motor RPM, motor Kv, Tube Volume, FSA, Wattage Motor Uses, number of rotors, Diameter of interior EDF tube, Diameter of Hub, Voltage, Air density, length of EDF.

I have the numbers for all these and that should be enough, that’s a lot of details.

If not can you explain what Velocity it’s talking about and also what Exhaust and free stream velocities are?

THANKS!

– ifconfig
Apr 4, 2021 at 19:39

The problem you have found is that you are trying to calculate the efficiency and lift coefficient of your fan, which isn't possible. There's no simple calculation to convert power to thrust because it will depend on the angle of attack of the blades to the airstream.

The mass flow rate is calculated on the velocity of air through the fan, not the motor speed.

The 'Free Stream' velocity is the air speed of the aircraft, or zero for a static test rig. You could measure the exhaust velocity with a pitot tube - a simple length of clear tube with some water held in a U-bend would work to compare static and dynamic pressure. However if you're measuring things, you might as well measure the thrust directly.

The alternative is to look up the thrust figures for commercially available EDFs, and scale them to allow for any difference in power (I'd guess that a 3D printed fan can't run as fast as a commercial unit)

Having said that, it must be possible to take the normal lift equation (1/2 * lift coefficient * air density * area * air speed squared) and treat the fan blades as wings and integrate for the change of speed with radius. I guess the problem is that you could estimate the maximum lift-coefficient to 1 but it could be 30% higher or lower, and you probably want a more accurate answer.

If you look on-line, you'll find a number of power-to-thrust calculators for RC propeller aircraft, but they all rely on measured values for specific propellers. I've not seen one that includes values for EDFs, presumably because EDF thrust is highly dependant on inlet and exhaust shape.

• As you say, taking the wing lift equation and integrating along the blade is not difficult. The chord being c and the radius r, you take an element of blade area ds=c·dr So, in differential form, the lift equation becomes dL = 0,5 · CL · v2 · c · dr · rho, with CL being the lift coefficient, v the airspeed at a blade station and rho the air density. Now you look up the data for the airfoil, and approximate CL as a linear function of the angle of attack AoA. For angular velocity w, AoA is written as a function of w and r. Inserting values, you get an easy to integrate polynomial in r2. Apr 6, 2021 at 9:38