# How can a small ducted fan produce a large amount of thrust?

This 15.2 cm ducted fan by Schuebeler can produce 175 Newtons of static thrust. How is this possible in such a small diameter?

If this seems normal, then why and how can this ducted fan produce that much force?

• When you pack too much thrust into a ducted fan it becomes a turbofan. – user3528438 Sep 28 '20 at 1:40
• A 16 hp motor to make only 40lbs of thrust is not all that impressive. A 16 hp motor driving a large prop would make about 50-60 lbs. It's only real benefit in the motoglider case is compactness. – John K Sep 28 '20 at 2:36

Thrust depends greatly on diameter, so your curiosity is reasonable.

Why: A first-principles answer says that (static) thrust depends directly on the rate of mass flow through the duct. Because the duct's area is small, the speed of air through the duct must be large, and thus what must also be large is the fan's (static) pitch speed and its RPM.

See https://www.grc.nasa.gov/www/k-12/airplane/thrsteq.html for the case $$p_e = p_0$$.

For 175 N thrust, Schuebeler says the fan turns at 20,000 rpm and needs 12 kW. Those numbers are not vastly different from an unshrouded 15 cm propeller, or a small turbine (a JetCat P220 does 220 N at 725 mL/min, converted via kerosene's MJ/L to roughly 450 kW; there's much more waste heat in a turbine's exhaust than in a ducted fan's gradually warming battery pack).

How: Tight manufacturing tolerances, so the blades don't vibrate from imbalance, so the blades don't deform or break at high rpm, and so not too much air leaks around the gap between the blade tips and the walls of the duct. (The same applies to turbines.)

• Oh thank you for the clarification. I also have another question from this. How much airflow must exist in order to provide this much force? – Ashutosh Lodd Sep 28 '20 at 13:31
• Static thrust = mass flow rate times exit velocity = (density of air) * (area of duct) * (speed squared), from grc.nasa.gov/www/k-12/VirtualAero/BottleRocket/airplane/…. There you go! – Camille Goudeseune Sep 28 '20 at 15:17