# Does adding mass to the fan blades affect its max velocity?

If I replaced fan blades with congruent blades, the only difference being the second set has a higher density, would that affect the speed cap on the spin? I know it would affect acceleration, but I am talking about the speed ceiling.

P.S. Assume the blades are made of extremely rigid material and cannot change shape or break off because of a reinforced base.

P.P.S. And I was also wondering if, with the same scenario, except with a plane. Would it go faster/slower?

• The drag forces wont change, so the situations appear to be congruent apparently – Lelouch Jul 13 '16 at 17:23
• Centripetal forces would increase. At high $v$ that might affect the upper speed limit, as higher stresses are needed to keep the fan 'together'. – Gert Jul 13 '16 at 17:55
• @Gert +1. We don't know what sort of "fan" the OP is thinking about, but the fan blades in a jet engine for example have radial accelerations of thousands of $g$ at maximum speed. Doubling the mass of a 10 kg blade would increase the radial force on the blade root by something of the order of 100 tonnes (for each blade!) not by a few kilograms of extra weight. The aerodynamic loads on the blades are small compared with the mechanical loads. – alephzero Jul 13 '16 at 22:46
• @alephzero `@Gert Assume the fan is reinforced at the base somehow – Adamawesome4 Jul 14 '16 at 19:52
• If you want to simplify your question, just assume the two sets of fan blades with different mass are made of (imaginary) infinitely strong and infinitely stiff materials with different densities. Then the "accepted answer" is correct. As well as the radial loads limiting the RPM, blades made from real non-rigid material will change shape because of the forces acting on them, so it would be hard to pin down exactly what you mean by "congruent". If the blades with different density were the same shape when not rotating, they would be different shapes when rotating at the same speed. – alephzero Jul 15 '16 at 0:19

## 1 Answer

No. As you realise, this will increase the moment of inertia, which will reduce angular acceleration since the torque which the motor can supply is limited. However, the maximum speed which the motor can reach is not affected, since this depends (mainly) on the aerodynamic force, which is the same - it depends on the shape and size of fan, but not its mass.

• There may be more friction at the bearings? – Farcher Jul 13 '16 at 19:25
• The rolling friction of bearings is not the limiting factor for speed. Torque to turn a bearing is probably 1/1000-th of the aero forces. – ja72 Jul 13 '16 at 19:55
• surely drag force is not the only factor in determining the speed cap? – Adamawesome4 Jul 14 '16 at 19:52
• @Adamawesome4 : Well the aero-dynamic force is the 'load'. (I may not be using the term 'drag' properly here.) Increased mass might also increase friction in bearings, but as ja72 suggests, this is negligible anyway. Do you have any other ideas in mind? – sammy gerbil Jul 14 '16 at 21:57