# How can I calculate the thrust of a fan given the diameter of the blade?

How do I calculate the thrust of a multicopter fan blade from its diameter?

I am searching for a multicopter blade that can provide a thrust of 15 - 20N.

Being someone who doesn't have any experience in avionics, I searched online for such blade believing that I could find the thrust the blade can provide, but every website for a multicopter wing, only the diameter is provided.

Is there a formula that provides thrust of a blade from its diameter?

• The thrust depends on other parameters than the diameter: speed of rotation and pitch angle being the most obvious. – mins Dec 13 '17 at 13:13
• I don't have any experience in Avionics, but the project I am doing, requires a rotor/fan/blade that can provide that thrust, I tried searching for a multi-copter blade, but I can only see the diameter of the blade in the specifications – Forat Dec 13 '17 at 17:10
• You may try to look at questions like this one: What is the highest possible thrust generated by 15cm ducted fan? – mins Dec 13 '17 at 17:35
• You can't. You need additional information. – user7241 Dec 13 '17 at 21:45
• Not according to the pulling disk theory, that is what causes the confusion. – Koyovis Dec 18 '17 at 9:51

I checked out your original post, and the Quora post referenced in it. The thing is that what is mentioned there is simple impulse dynamics: there is a magic disk with no drag that accelerates air going through it. It's a theory that works if you realise the limitations, allows for quick ROM estimations, and can provide even more useful info when some drag effects are included in the form of propeller/rotor efficiency. The Quora post is not incorrect, but it is a simplification and it is valid for a different scale.

For a magic disk, all you need to know is the disk area, it does not even need to have a mounting axis. For a real propeller/fan that is not optimised yet, the following parameters need to be considered:

• Rotor RPM, together with the blade radius resulting in tip velocity.

Between your application and the Quora helicopter disk, there are the following differences that need to be catered for:

• Your rotor is small. Reynolds effects start playing a big role here, with a much thicker boundary layer. Departs further from the impulse theory than an average helicopter rotor: increases power demand.
• Your rotor is ducted: reduces power demand by about 35% for small rotors, see figure below.
• Your rotor is a fan: increases power demand. Every added blade requires proportionally more power for a an increase in thrust that gets smaller with every blade.
• Your rotor has difficulty bringing the air in. A curved duct restricts incoming air flow, increasing power demand and putting a cap on maximum thrust.

So we need to use data from small scale rotor research. Here is a masters thesis researching just that, unfortunately with an underpowered motor so the results are only valid for low Mach numbers. If we look at the highest Mach number in the graph and compare data points for Thrust = Lift, we can see an increase in $C_T$ (is a measure for thrust) of 0.047/0.035 = 35%.

$C_T$ is defined here with reference to the ducted fan wetted area, and it is not very clear which units are used. There is a graph of thrust force vs. rotor rpm:

6000 rpm with a 9.5" rotor equates to a tip Mach of 0.22. Propellers can run with a tip speed of up to 0.75 Mach before compressibility effects occur, that would be 20,000 rpm for this configuration. Extrapolating the curve to 20,000 rpm would result in about the 15 - 20 N mentioned in the OP.

It's a 3-blade rotor. Thrust can be further increased by increasing blade pitch and increasing number of blades, each increase requires an increase in power as well. Unfortunately the research does not mention power required for each thrust config found, but:

• Appendix A has some provisional power curves for other rotors used in the project. It also mentions the use of a gearbox to increase rotor rpm, something OP may wish to consider as well.
• A table with a motor trade study used in earlier research is included, outlined below.