# Powering and Propeller Sizing

By examining data from propeller manufacturers and their recommendations, it is possible to derive a simple regression curve that allows probable propeller diameter to be derived from engine capacity and likely pitch from diameter:

D(in.) = 4.239Cap(cu. in.)^{2} + 11.096Cap(cu. in.) + 14.616 P(in.) = 0.516D(in.)

Item Typical no. Possible dependency

**Table 11.5 **Items for which weight estimates may be required and possible dependencies.

Item |
Typical no. per a/c |
Possible dependency |

Wing spars (incl. center spars) |
2 |
Wing area, spar length, speed |

Wing ribs+ nylon parts |
6 |
Wing cross-sectional area |

Wing foam |
2 |
Wing box volume |

Wing covers |
4 |
Wing area |

Ailerons |
2 |
Wing box volume |

Flaps |
2 |
Wing box volume |

Tail boom |
2 |
Tail-plane area, spar length, speed |

Tail fin |
2 |
Individual fin area |

Tailplane |
1 |
Tail-plane area |

Rudder |
2 |
Individual fin area |

Elevators |
1 |
Tail-plane area |

Engine |
2 |
List of engine weights |

Muffler |
2 |
List of engine weights |

Propeller |
2 |
Prop dia. |

Generator |
2 |
Engine mass/?fixed |

Ignition unit |
2 |
Engine mass/?fixed |

Fuel tank |
0 |
Engine mass/?fixed |

Aileron servos |
2 |
Wing area |

Flap servos |
0 |
Wing area |

Throttle servo |
1 |
Engine mass/?fixed |

Rudder servo |
2 |
Individual fin area |

Elevator servo |
1 |
Tail-plane area |

Wheel steering servo |
2 |
Wing area |

Linkages and bell-cranks |
8 |
Total wing area/?fixed |

per a/c

Also, one can estimate the likely engine capacity from engine power by looking at a range of small engines to get

Cap (cu. in.) = 0.0189(Power (kW))^{2} + 0.9288Power (kW).

Then the (uncorrected) Abbott equations^{[1]} link power, thrust, pitch, diameter, and rotational speed as:

Power(W) = P(in.) x D(in.)^{4} x rpm^{[1]} x 5.33 X 10^{-15 }StaticThrust(oz.) = P(in.) x D(in.)^{[1]} x rpm^{2} x 10^{-10}.

**Table 11.6 **Other items for which weight estimates may be required.

Item |
Typical no. per a/c |

R/C receiver |
1 |

Batteries |
2 |

Autopilot |
2 |

Misc. avionics |
1 |

Wiring and aerials |
1 |

Engine covers |
2 |

Main fuselage |
0 |

Rear nacelle fuselage |
2 |

Mid-wing skin & fuel tank |
1 |

Rear wing box |
1 |

Nose |
2 |

Front bulkhead |
2 |

Main undercarriage structure |
2 |

Main wheels |
2 |

Undercarriage mounting point |
1 |

Catapult mounting |
1 |

Tail undercarriage structure |
2 |

Nose undercarriage structure |
0 |

Tail wheels |
2 |

Nose wheel |
0 |

Therefore, we can eliminate rpm to link thrust to power:

StaticThrust(oz.) = (D(in.) x P(in.))^{1/3} x *(Power(W)/5.33E -* 15)^{2/3} X 10^{-10}.

So, given an engine power, we can estimate its likely static thrust when matched to a suitable propeller. Since we can also estimate the required thrust for cruise, banked turns, climb, and takeoff as described in the previous chapter, it is then possible to make an engine selection given the overall aircraft weight. For example, the estimated thrust needed for takeoff is given by

where the three terms represent the kinetic energy required during the ground roll, the mean aerodynamic drag on the runway, and the mean rolling resistance on the runway (recall that here *q* is the dynamic pressure at 70.71% of the take-off speed V_{L}). The estimated thrust for climb is given by

where *V _{V}* is the vertical velocity in the climb and

*k*is the lift-induced drag factor.

Next, using the UIUC Propeller Data Site,^{[4]} variations in propeller thrust with airspeed for a given diameter and rotational speed can be deduced by regressing plots of the thrust coefficient C_{T} versus the advance *J.* For example, for thin electric propellers with 12 in. pitch, the thrust coefficient can be approximated from the advance ratio as C_{T} = 0.4876J^{[4]} - 0.6571J^{3} +

0.0629J^{2} + 0.0101 J + 0.0900. It is also possible, using JavaProp (and a suitable base propeller design operating at fixed torque), to calculate static thrust and to derive regression curves for thrust and required power as the forward velocity changes. In either case, these can be used to simulate runway roll-out and initial climb to check the results from the above equation and also to check whether the assumed propulsive efficiency is sensible. However, when the design is close to balance, we need to recognize that only existing engines can be specified and one should then switch to data for actual engines. Figure 5.3 given previously shows the powers and thrusts of typical UAV engine/propeller combinations.

- [1] http://www.rcgroups.com/forums/archive/index.php/t- 1217933.html
- [2] http://www.rcgroups.com/forums/archive/index.php/t- 1217933.html
- [3] http://www.rcgroups.com/forums/archive/index.php/t- 1217933.html
- [4] http://m-selig.ae.fflinois.edu/props/propDB.html.
- [5] http://m-selig.ae.fflinois.edu/props/propDB.html.