Re: Prop Efficiency

From: markdrela <drela_at_mit.edu>
Date: Tue, 29 Aug 2006 15:31:38 -0000

--- In Indoor_Construction_at_yahoogroups.com, "John Kagan"
<john_kagan_at_...> wrote:
>
> I measured up one of my better props.
> This is low pitch, which should correlate to about .1in/oz of
> torque and about 50rpm. High pitch is about 5 degrees higher,
> around .3in/oz, and 45rpm.

Your blade angles look way too small. The tip angle implies P/D =
1.00 . I assume they have a large jig offset.

Anyway, I had to add 12 degrees to get the low-pitch torque (0.1
in-oz) and RPM to match up. The resulting thrust is 0.40g, implying a
slight climb (my estimate of level-flight thrust is 0.36g). The
blade cl's look pretty good in this low-pitch condition:

# V(m/s) rpm Dbeta T(N) Q(N-m) Pshaft(W)
Volts Amps effmot effprop adv
# 0.670 50.17 0.000 0.3915E-02 0.7060E-03 0.3709E-02
0.362 0.7908 0.0130 0.7071 0.50205
#
# radius chord beta Cl Cd Re Mach effi
  effp Wa(m/s) Aswirl adv_wake
   0.0424 0.0188 64.838 -0.1978 0.13545 913 0.002 1.0131
 3.9421 0.6691 -0.2238 0.4956
   0.0511 0.0290 62.953 -0.1986 0.10197 1439 0.002 1.0174
 2.8589 0.6684 -0.3423 0.4935
   0.0597 0.0367 61.563 -0.1101 0.07744 1869 0.002 1.0108
 3.7266 0.6687 -0.2363 0.4967
   0.0683 0.0430 60.256 0.0359 0.06895 2250 0.002 0.9963
-1.2842 0.6706 0.8826E-01 0.5039
   0.0770 0.0481 58.879 0.1569 0.06388 2593 0.002 0.9833
 0.2529 0.6730 0.4247 0.5106
   0.0856 0.0519 57.523 0.2634 0.06137 2882 0.002 0.9717
 0.5580 0.6758 0.7574 0.5167
   0.0942 0.0549 56.144 0.3535 0.06040 3145 0.002 0.9617
 0.6774 0.6790 1.064 0.5221
   0.1029 0.0575 54.814 0.4337 0.06021 3407 0.003 0.9524
 0.7403 0.6824 1.358 0.5271
   0.1115 0.0599 53.507 0.5026 0.06040 3666 0.003 0.9439
 0.7773 0.6861 1.633 0.5319
   0.1201 0.0613 51.721 0.5248 0.05953 3883 0.003 0.9405
 0.7923 0.6886 1.750 0.5338
   0.1288 0.0621 49.545 0.5080 0.05752 4070 0.003 0.9414
 0.7953 0.6898 1.730 0.5333
   0.1374 0.0627 47.474 0.4896 0.05566 4248 0.003 0.9423
 0.7961 0.6908 1.702 0.5328
   0.1461 0.0625 45.900 0.5001 0.05518 4379 0.003 0.9402
 0.8022 0.6929 1.758 0.5340
   0.1547 0.0618 44.693 0.5301 0.05565 4475 0.003 0.9359
 0.8109 0.6958 1.874 0.5364
   0.1633 0.0608 43.354 0.5424 0.05565 4550 0.003 0.9334
 0.8143 0.6981 1.930 0.5379
   0.1720 0.0589 41.370 0.5012 0.05415 4553 0.003 0.9376
 0.8046 0.6974 1.783 0.5355
   0.1806 0.0563 39.467 0.4601 0.05316 4498 0.003 0.9421
 0.7914 0.6964 1.626 0.5329
   0.1892 0.0535 38.177 0.4581 0.05361 4413 0.004 0.9419
 0.7875 0.6974 1.607 0.5330
   0.1979 0.0505 36.892 0.4504 0.05408 4300 0.004 0.9421
 0.7808 0.6981 1.575 0.5329
   0.2065 0.0472 35.417 0.4233 0.05435 4137 0.004 0.9446
 0.7657 0.6975 1.477 0.5315
   0.2151 0.0433 34.085 0.4018 0.05529 3913 0.004 0.9465
 0.7492 0.6972 1.400 0.5304
   0.2238 0.0389 33.400 0.4235 0.05810 3620 0.004 0.9427
 0.7474 0.6998 1.476 0.5326
   0.2324 0.0329 32.508 0.4276 0.06242 3150 0.004 0.9420
 0.7316 0.7008 1.467 0.5330
   0.2410 0.0242 31.044 0.3900 0.07046 2384 0.004 0.9491
 0.6791 0.6974 1.255 0.5290
   0.2497 0.0123 29.632 0.3570 0.09617 1244 0.004 0.9584
 0.5689 0.6927 0.9989 0.5238


The high-pitch case you give has 3x larger torque, and RPM reduced to
45. This is possible only if the blades are massively stalled. It's
not possible (and kinda pointless) to calculate this case, because the
blade airfoil cl and cd curves are very uncertain so far past stall.

In general, VP props are an aerodynamic disaster, in the sense that
they work by blowing off the torque burst in the form of blade drag.
To maximize duration, it would be much better to keep the blades
unstalled, but reduce the RPM *way* down, roughly in inverse
proportion to the torque (thrust would still be roughly the same).
The only way to do this is to increase the diameter greatly, but of
course that has lots of practical problems.
Received on Tue Aug 29 2006 - 08:38:38 CEST

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