HW 6: Electric Propulsion

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For the starter design in FlightLab, choose an appropriate propeller, motor and battery (from the list provided in FlightLab). Some of the key metrics are listed below.

• aircraft mass: 0.80 kg (weight 7.85 N)
• cruise speed: 12 m/s
• air density: 1.07 kg/m^3
• drag at cruise: 0.81 N

All of these parts are listed in FlightLab but are repeated below.

Motor	Kv (RPM/V)	R (ohm)	I0 (A)	current limit (A)
SunnySky X2216 II KV1100	1100	0.073	0.90	24
SunnySky X2208 KV1260	1260	0.122	0.40	15
SunnySky X2216 II KV1400	1400	0.055	1.30	33

Battery	cells	capacity (mAh)	internal resistance (ohm)
Turnigy 2S 1500 mAh	2	1500	0.020
Turnigy 3S 1000 mAh	3	1000	0.039

Propeller	diameter (in)	pitch (in)	rpm limit	UIUC data file
APC 8x6E	8	6	23,750	apce_8x6_2799rd_5015.txt
APC 9x4.7SF	9	4.7	7,200	apcsf_9x4.7_kt1034_5013.txt
APC 10x4.7SF	10	4.7	6,500	apcsf_10x4.7_rd0838_4997.txt

The data files are from the UIUC Propeller Data Site. Each has four columns: J, CT, CP, and η. Use the file linked for each propeller (UIUC measured each propeller at several rpm; these runs are near the middle of the range and cover the cruise condition). Interpolate within the table.

6.1: Rough Size by Hand

In this first problem we’ll do some rough sizing by hand (using code).

• (a) Propeller. For each of the 3 propellers:
  • use the CT curve to figure out the rotation speed required to produce the cruise thrust (0.81 N, one propeller)
  • look up the efficiency corresponding to that advance ratio
  • choose the one with the highest efficiency at your requisite thrust
• (b) Motor. Now that you know the rotation speed and torque your motor must provide, you can choose a motor that will be efficient at those conditions. For each of the 3 motors:
  • Compute the current, supply voltage to the motor (Vm), and efficiency.
  • choose the one with the highest efficiency

• (c) Battery. You need some extra capacity to climb, so let’s design the cruise at roughly 70% throttle. That means your battery voltage will need to be at least Vm/0.7. Determine roughly how many cells you need in your battery for that voltage level (assume 3.7 V per cell as a typical nominal voltage for LiPo batteries).

• (d) Endurance. Calculate the current for the battery (not the same as the motor since we are not at full throttle). The speed controller passes power through (minus a small efficiency loss we ignore in these hand calcs), so we can compute battery current directly from the known required power (P = Vm Im). Then we can determine battery voltage. The 70% in (c) was only a target for choosing the cell count; the actual cruise throttle is t = Vm / Vb (equivalently Ibatt / Im). Then determine how much of your battery capacity you would use for 15 minutes of cruise.

6.2 Verify in FlightLab

Use the new starter design (you’ll need to click it as it starts with the multi-panel design). On the Propulsion tab set the battery state of charge to 0.4. FlightLab’s battery voltage depends on state of charge, and 0.4 puts it at the nominal 3.7 V per cell we used in this example. Load up your propulsion system choices and run the propulsion analysis.

Compare the cruise row with your numbers from 6.1. They should be quite close but not exactly the same (FlightLab interpolates across Reynolds numbers in the propeller data, includes a loss of efficiency from the speed controller, and the drag, and thus the required thrust, changes a bit because FlightLab updates the aircraft mass as the propulsion components change).

That’s all we’ll do in this homework, but when you are designing your own system you’ll want to do some more checks, and potentially some more iterating (finding the best component one at a time doesn’t necessarily lead to the best combination overall). Some additional checks you might consider:

• at full throttle, check that the motor current does not exceed its limit, and check that the propeller rpm does not exceed its limit (or determine a limit on throttle to set in the transmitter). Motor current is highest at zero airspeed, but propeller rpm is highest at high airspeed where the propeller unloads, so check the whole speed range, not just the static case. FlightLab’s warnings cover both.
• check the speed controller’s current rating and the battery’s maximum current (its C rating times its capacity) against the full-throttle current
• check that you have sufficient thrust for a hand launch (full throttle, static case). As a rule of thumb you probably want static thrust equal to about half the aircraft weight or more.
• check that you have sufficient energy for several flight attempts while using less than 80% of your battery capacity. In 6.1(d) we only checked cruise. Add a minute or two at full throttle to account for hand launches and climbs.
• check that thrust minus drag at your climb speed gives an acceptable rate of climb
• the propulsion components are a large fraction of the aircraft mass and the battery is usually the heaviest single item, so revisit the mass and CG (and trim) after choosing them, and weigh an extra battery cell against the drag its mass adds.