

Thread OP

Question
Prop size and efficiency
I was originally planning a 4S power system for my 40" wing but due to size and layout constraints have decided to go with 3S instead. My motor is a Cobra C2221/12 (1250kV), and I was originally planning to use APC 8x6E props. I am thinking going to 9x6 props instead now that the power system will be 3S, in the hope of getting better efficiency and longer flight time as the wing is intended for moderate range flights. I had expected that the larger, less aggressive (in terms of pitch angle) 9x6 prop would give greater efficiency.
However when I run this in eCalc, it gives me the opposite prediction. For an AUW of 1100g, it predicts an endurance of 56.2 minutes at 36 mph on a 5000mAh battery with the 8x6E prop. The same configuration with a 9x6E prop has a predicted endurance of only 34.7 minutes at the same airspeed. The difference seems to result from different prop efficiencies, 8.6 g/W for the 8x6 vs only 7.6 g/W for the 9x6. Motor efficiency is essentially identical for the two props. There's some difference in pitch speed  64 mph for the 8x6 vs. 60 mph for the 9x6. However since prop efficiency is generally highest close to the pitch speed, I would expect this to favor the 9x6 prop. The trend seems to continue  with a 7x6 prop it is showing an endurance of 91.9 minutes at 35mph. I find it difficult to believe this! I note that the Cobra motors prop charts show the 9x6E to be the more efficient prop, giving 1200g thrust at 4.27g/W, compared to the 8x6E which gives 1011g at 3.91 g/W. Admittedly these are static tests at maximum thrust, not unloaded props at cruise thrust. Does anyone have any insights into this? I'm not sure whether it's simply an eCalc error, or is the 8x6 prop really going to be more efficient than the 9x6? Thanks, Andrew 

Last edited by RFEngFPV; Jan 04, 2018 at 08:19 AM.





you changed the PD ratio, so it's not a realistic comparison. 8X6 is roughly 1.33 ratio (pitch of 6 times 1.33 equals diameter) 9X6 is 1.5 ratio. since duration for a given speed (36mph) is your goal,.. you should be able to find a higher pitch 9 inch dia prop that will get you there at an even lower throttle setting and result in longer flight times. APC has a 9X7.5"E" prop and I ran a simulation with motocalc. I don't have the same plane created in motocalc and I just used another motor around that KV and size so although the numbers aren't realistic for your plane, they're a good apples to apples comparison of different props. checking with 8X6.9X6.9X7.5, and reducing throttle to maintain cruise speed of 36mph the 8X6 is predicted to cruise for 96 (57% throttle) minutes, the 9X6 for 89 minutes (64% throttle), and the 9X7.5 although higher static current draw is predicted to cruise for 100 minutes at 51% throttle.
Efficiency is not simply comparing flight times. Efficiency is how much work you get out of the system for a given amount of work going in. The 9X6 will have more "1st gear" or thrust to get going but at level cruise it's not the optimal choice. The 8X6 will have less 1st gear but a bit more 5th gear, more efficient at cruising speed with throttle reduced. When you go up in diameter, you have to also go up in pitch to retain the same ratio of pitch to diameter, or, if you want more efficiency you tweak the PD ratio a bit. Also have to do that because we don't have a lot of completely adjustable pitch props to get it perfect I'll make a car analogy. With the 8X6 it's like driving down the highway in 5th gear,.. very good for what's needed, but not good if you're starting from a dead stop, going up a hill. The 9X6 is better for the start and acceleration but when you get on the highway, you're trying to cruise in 1st gear. Actually, the two are much closer than that example but i exaggerated to make the point more clear 
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Thread OP

Thanks GWRIGHT for your detailed response, it really gave me something to think about.
In order to make sense of it, I took the prop data files from the APC website and used them to graph the efficiency of the 8x6E, 9x6E and 9x7.5E at 36 mph. I included the 9x7.5E as it has a PD ratio of 1.2, so the 9x6 has a higher PD ratio than the 8x6 as you pointed out, while the 9x7.5 has a lower PD ratio. The APC data is simulated not measured, but uses a much more sophisticated simulation system (based on fluid dynamics using the actual prop geometry) than eCalc. I used linear interpolation between the highest airspeed below 36 mph and the lowest airspeed above 36 mph to estimate the efficiency and thrust at 36 mph. Since I don't know exactly how much drag the airframe will generate, I plotted the efficiency against thrust for each of the props, which I converted to grams. Note that the APC files give actual (power) efficiency, a dimensionless number, not the "g/W" figure which is sometimes referred to as efficiency. I've attached the resulting graph. It shows that both 9" diameter props should be more efficient than the 8x6 provided the required thrust is greater than about 200g. The 9x7.5 is more efficient than the 9x6 provided the thrust required is less than 600g. I expect that the thrust required will be between 200g and 600g (which corresponds roughly to a lift/drag ratio of between 6:1 and 2:1), so the 9x7.5 should be the most efficient prop, the 9x6 the second best, and the 8x6 the least efficient. For the 9" props this corresponds to the different "gearing" as you put it. When comparing the 8" and 9" props another factor comes into play, which is the additional tip vortex drag of the smaller diameter prop. I think the reduced efficiency of the 9x6 at low thrust values is probably due to the prop pitch speed becoming less than the airspeed, resulting in the prop blades being operated at a negative angle of attack. Interestingly, eCalc gives differing figures for thrust at 36 mph depending on what prop is selected. I find this difficult to believe  the thrust required should be equal to the drag, which should depend on the mass and lift/drag ratio of the airframe but not, I think, on the prop size. For example, for the 8x6 prop it suggests that 429g thrust is required for 36 mph cruise; wheras for the 9x6 prop it says that 610g is required for the identical airframe. I've reported this to Markus and he will look into it when he returns from vacation. I also ran a 9x6.75 prop on eCalc, which would have the same PD ratio as the 8x6. It gives a motor run time of 47.6 minutes at 35 mph, which is still less than the 58.4 minutes that the 8x6 prop gives at 36 mph. This discrepancy obviously can't be explained by PD ratio as they are the same. 




Thread OP

I've published a more detailed analysis, including prop efficiency charts for 40 kph and 80 kph, in Choosing a Prop for my 40" Wing.





Thread OP

I thought I should report the resolution of this in case anyone else has a similar issue.
Markus, the author of eCalc, informed me that the "simplified" drag model in eCalc assumes that the fuselage frontal area is approximately 90% of the area of the propeller disc. So when I increased the prop diameter, eCalc assumed a larger frontal area, and the drag went up accordingly. So if you want to compare different diameter props on the same aircraft, you need to use the "coefficient" drag model with the actual frontal area of the aircraft. 





rc
I took the prop data files from the APC website and used them to graph the efficiency of the 8x6E, 9x6E and 9x7.5E at 36 mph. I included the 9x7.5E as it has a PD ratio of 1.2, so the 9x6 has a higher PD ratio than the 8x6 as you pointed out, while the 9x7.5 has a lower PD ratio.






Quote:
note that the propeller disks of different diameter propellers will have different areas , affecting the drag. 





Thread OP

I would agree for a windmilling prop or one being driven at a pitch speed that is slower than the airspeed. However under cruise conditions, the prop's pitch speed exceeds the airspeed, and the prop should have negative drag (i.e. thrust). Of course the prop blades do have drag, but all things being equal I would expect that a larger prop blade would have lower induced drag due to smaller tip vortex, as is borne out by the APC prop efficiency graphs that I posted above.






I tried putting in values for coefficient, but still get the same discrepancy between larger prop (same ratio) with lower kv vs smaller prop with higher kv.
I checked drive calc (doesnt give as detailed info  no level speed at specific throttles and run time etc), but it gives the WOT run time as being lower with the same battery and lower kv with bigger prop too. 


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