# What is the highest possible thrust generated by 15cm ducted fan?

I recently developed a sudden interest in flying. I'm wondering whether a pair of small ducted fans could lift a person off the ground.

Lets say the ducted fan is 15cm in diameter. What would be the most thrust a fan like that could produce?

• Thrust is directly related by flow rate in your setup, which is limited to chocked flow. – Sanchises Jun 29 '15 at 8:04
• @sanchises "Choked" flow. "Choked" means restricted by flow area; "chocks" are also used in aviation: they're the wedges you put around wheels to stop vehicles rolling away. – David Richerby Jun 29 '15 at 8:38
• @DavidRicherby Oops... I guess chocks can be a limiting factor for most aircraft engines as well... ;) – Sanchises Jun 29 '15 at 10:06
• @sanchises Chocks aren't so much a limitation for helicopters, though. :) However, they could still be a problem for whatever (or whoever) gets hit by them as they get blown away by the rotor wash. – reirab Jul 1 '15 at 13:44
• Perhaps you should look into one of these: en.wikipedia.org/wiki/Martin_Jetpack – PJNoes Jul 1 '15 at 19:16

A 15cm diameter fan could maybe lift 4 KG of mass with a tip speed of 0.6M.

By increasing the power and the blade chord length (in other words, increasing the solidity of the rotor), this may be increased to maybe 6KG or more, but a single fan would probably never lift more than 10KG mass.

The thrust of a rotor is $CT \cdot \rho \cdot Area \cdot tipSpeed^2$.

• $\rho$ = air density (1.225kg/m^3 at sea level).
• $Area$ = area of rotor disc (m^2)
• $tipSpeed$ = the linear speed at the tip of the rotor = radial speed * radius.
• $CT$ = coefficient of thrust. (is usually in the order of 0.02 to 0.05 for small rotors)

Assuming $CT$ of 0.03, the calculation shows 40N (=4 KG) thrust.

Disc area is one of the most important parameters, even a 30cm disc would generate 4 times the thrust. 60cm would make almost 65 KG.

Apparently, a 50cm diameter disc can possibly generate 45kg thrust on its own. So two of them could carry and maybe even lift-off a person equipped with this backpack (the person + the system must be less than 90 KG).

• Thank you for being for thorough in your answer. Lets say there are two ducted fans each 20cm in diameter. Utilizing the best technology and engineering could we squeze out over 60kg of thrust out of them? – Alexander Yurchenko Jul 2 '15 at 21:12
• I found this NASA's research on magnetically levitated ducted fans here: ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070006851.pdf Is it more efficient, thrust power wise, than a regular ducted fan? I wonder if there where two 20cm in diameter versions of this design would that be enough? – Alexander Yurchenko Jul 2 '15 at 21:16
• I saw the 0.02 to 0.05 CT values as results of some tests in a rotor design paper. My assumption was 0.03 and with squeezing, that might maybe become 0.06, which is double the numbers I've given. 20cm diameter would not give enough thrust. You could play with the numbers. thanks for accepting this answer. – Gürkan Çetin Jul 2 '15 at 21:31
• I'm trying to write out the equation. And not really getting the same results. In the equations where you got 4kg of thrust (with the 15cm diameter) what did you use for your RPM? – Alexander Yurchenko Jul 3 '15 at 23:40
• in my sample calculation, the tip speed was M0.65 = 215 m/s. That means a radial speed of 215 / 0.075 = 2866 rad/s. which happens to be more than 27000 RPM. quite a huge number. – Gürkan Çetin Jul 4 '15 at 4:48

## Calculating Thrust

One design required sixteen 20-inch (~50 cm) propellers to lift a person.

These were unducted but I doubt that any 15cm ducted fan produces more thrust than eight 50cm propellers can.

See Autonomous human transport for details of how the designer calculated thrust.

He used Thrust (pounds) = R2D4Tc where Tc is an empirically measured constant for which he had a value of 2.7734 x 10-12. R is RPM, D is diameter (inches).

I imagine max RPM might be limited by the need to keep the fan tips subsonic (e.g. < M0.5).

Note that thrust is shown as depending on the fourth power of diameter, sixteen 50cm propellers will therfore produce about 1000 x the thrust of two 15 cm propellers of the same design at the same RPM.

## Ducted vs Free

It seems you need to be careful when comparing ducted fans with propellers. Using higher RPM to compensate for smaller diameters results in lower efficiencies (you need bigger motors).

Small diameter, high disk loading ducted fans are often conceived to allow the use of a high rpm engine running a direct drive propeller. While these highly loaded fans (if properly designed) will be more efficient than a free propeller of the same diameter, they typically wonâ€™t match the efficiency of a larger free propeller (of much lower disk loading)