Postscript
Measurements with my FOHDY show that the 9×6 prop peaks at about 36A static at full throttle, and draws 28-32A or so during a slow, high-power climb with a full battery. I think that’s quite enough for my C-2221/12 motor (which is rated 32A continuous), so have decided to use the 9×6 not the 9×7.5. The 9×6 combines good takeoff and climb performance with reasonable cruise efficiency, so it’s a good general purpose prop. See the graph below, which shows current consumption (red, A) and altitude (green, m) during takeoff and climb out.These figures also include the current consumption of the flight controller, FPV camera and video transmitter, which total to about 300 mA.
The original post is below….
Having decided on 3S power, I need to decide what prop to use. The principle use case for this aircraft is a medium range cruiser, so I decided to evaluate prop choices primarily in terms of efficiency. In order to determine prop efficiency one needs to know how much thrust the prop will be required to produce at each airspeed. For constant speed flight this is equal to the drag.
I calculated this (roughly) using the spreadsheet on this How To Calculate Drag page, courtesy of JonnyB. I used a conservative all-up weight of 1200g which gave the following result:
Since I’m generally pessimistic (and because the wing will be carrying a Foxeer Legend HD camera which is not included in the drag calculation), I’m going to interpret this calculation as a lower bound, and assume that the upper bound is 50% more than the calculated drag. In other words:
- At 40 kph drag will be between 160g and 240g;
- At 60 kph drag will be between 220g and 330g;
- At 80 kph drag will be between 320g and 480g;
RPM314 on RCGroups kindly gave me access to his model aircraft performance calculator. I used it to plot drag and lift/drag curves for the Fohdy. The X axis is airspeed, in m/s. The green line is total drag, in units of 100g. The orange line is the lift/drag ratio. The red shaded area to the left indicates that the airspeed is below the calculated stall speed (9.3 m/s or 33.5 kph). Click here for a larger version.
Reading from this graph we get
- At 40 kph (11.1 m/s) drag is 185g.
- At 60 kph (16.7 m/s) drag is 240g.
- At 80 kph (22.2 m/s) drag is 370g.
These figures are slightly higher than predicted by JonnyB’s spreadsheet, but all fit within the additional 50% that I allowed above.
I then wrote an Octave script to analyse the propeller data supplied by APC and plot efficiency as a function of thrust for various propellers. I ran this for three airspeeds: 40 kph, 60 kph and 80 kph to represent slow, medium and fast cruise speeds. The calculated efficiency is the ratio of power generated by the prop to power required to drive the prop, which is a dimensionless number – it’s not the “g/W” figure that is often referred to as “efficiency”.
At 40 kph the required thrust is expected to be between 160g and 240g. From the graph we can see that the best prop over this range is the 9x9E, and the second best is the 9×7.5E.
At 60 kph the thrust requirement is expected to be between 220g and 330g. Again, the 9x9E is the most efficient prop and the 9×7.5E is the next most efficient.
Finally, at 80 kph the thrust requirement is expected to be between 320g and 480g. Once again the 9x9E comes first with the 9×7.5E the runner-up.
So the best choice in all instances would appear to be the 9x9E. However other factors comes into play here. eCalc shows that the 9x9E is partially stalled below about 44 kph, and will not generate full thrust. This is problematic as I estimate the airframe stall speed to be around 30 kph, so from 30-44 kph the airframe would be flying but the prop would not be generating full thrust, which could make it difficult to accelerate out of this airspeed range. This could especially be a problem during launch. In comparison, the 9×7.5E is only stalled below about 23 kph, which is well below the expected stall speed of the airframe and therefore less problematic. Also, at max throttle the 9x9E will consume about 90% of the Cobra 2221-12’s rated power, which leaves little safety margin; while the 9×7.5 will only consume about 80% of maximum rated power, which I am more comfortable with.
For these reasons I chose the 9×7.5E prop rather than the 9x9E. The efficiency difference is quite small, at most a couple of percent.
Finally, here are the eCalc results for the 9×7.5E prop. Click here for the full size image.
If you’re an eCalc subscriber, you can modify the parameters here.
Incidentally, the drag figures can also be used to estimate the range of the aircraft. The energy available from the battery can be calculated by
E = v i t
= 3600 v C
Where E is the energy available (J), v is the battery voltage (V), i is the current that can be drawn from the battery for a certain period (A), t is the time for which that current can be drawn (s) and C is the battery capacity in Ah. The constant value 3600 is the number of seconds per hour, used to convert the battery capacity from Amp-hours to Amp-seconds. The work required to move the aircraft at constant speed over a distance is
W = F D
where W is the work required (J), F is the force exerted (N) and D is the distance over which the force is applied (m). However work is related to energy by the power system efficiency η (dimensionless), so
3600 η v C = F D
dividing through by F,
D = 3600 η v C / F
We can estimate the Fohdy’s range at a constant 60 kph using the following values:-
η = 0.5 (power system efficiency including prop, motor, ESC and wiring)
v = 11.1 V (nominal voltage of a 3S battery)
C = 5.2 Ah
F = 3.24N (330g drag at 60 kph converted to N)
Then by calculation,
D = 32 067m
So as a very rough estimate, the range of the Fohdy (without reserves) should be around 32 km at 60 kph. Note that this does not take into account the energy used climbing to altitude or to supply non power system electronics such as the radio and video transmitter.