Electric: power+rpms=flight time (How long can I fly?)

[gwright]

Something to think about regarding the power put into a machine at the rpms some of you guys use. To increase rpms the input power increases exponentially, not linearly. For instance,.. say I fly at 2000 rpms and you fly at 2200 rpms. Many will think that's only a 10% increase, so it should take 10% more power. Many of us know this to not be true, but I've never known the "real relationship". A very smart friend of mine who is an engineering type, explained the power relationships and it's rather eye-opening. To make the above change actually requires 33% more power (1.33 times the original input power). The formula works like this,... you divide the new rpm by the old rpm, CUBE the difference, and multiply times the input power. I threw together a little spreadsheet to demonstrate, using my logo 10 setup (the one that will fly old/smooth style 3D for 9+ minutes but not the radical stuff you guys do these days). At 2000 rpms, I average 525 watts, or 28 amps on a 5S 4500 pack. The spreadsheet shows that going up to 2100 would mean 1.16 times the current input power ((2100/2000,.. which is 1.05) to the third power), which is 1.16. Going to 2200 takes 1.33 times the input, etc, etc. Flight times go down relative to current, so going from 2000 to 2100 takes me down from 9.5 to 8.2 minutes. Going to the "normal" (at least these days) 2500 rpms, would roughly half my flight time to 4.9 minutes. It can be said that the increased revs will require less pitch, which is true, but load difference from the tiny pitch change is minuscule compared to the load increase of rpms so it's virtually irrelevant.


current watts, rpm, new rpm, multiplier, new watts, cells (*3.7), capacity(mah), current, new current, flight time, new flight time

525 2000 2100 1.16 608 5 4500 28 33 9.5 8.2
525 2000 2200 1.33 699 5 4500 28 38 9.5 7.1
525 2000 2300 1.52 798 5 4500 28 43 9.5 6.3
525 2000 2400 1.73 907 5 4500 28 49 9.5 5.5
525 2000 2500 1.95 1025 5 4500 28 55 9.5 4.9
525 2000 2600 2.20 1153 5 4500 28 62 9.5 4.3
525 2000 2700 2.46 1292 5 4500 28 70 9.5 3.9
525 2000 2800 2.74 1441 5 4500 28 78 9.5 3.5
525 2000 2900 3.05 1601 5 4500 28 87 9.5 3.1
525 2000 3000 3.38 1772 5 4500 28 96 9.5 2.8

Here are the important fields, a little more readable

rpm, new, multiplier, flight time, new flight time

2000 2100 1.16 9.5 8.2
2000 2200 1.33 9.5 7.1
2000 2300 1.52 9.5 6.3
2000 2400 1.73 9.5 5.5
2000 2500 1.95 9.5 4.9
2000 2600 2.20 9.5 4.3
2000 2700 2.46 9.5 3.9
2000 2800 2.74 9.5 3.5
2000 2900 3.05 9.5 3.1
2000 3000 3.38 9.5 2.8

[DebianDog]

Thanks Gary!

[Klinger]

Knew it wasnt linear but to see the actual figures is great, good work!

[MrMel]

NICE!!!

And this is why you want VStabi/CSM/Flybarless.. you can lower headspeed and keep cyclic rate :) You gain alot.

[Lorents]

Great info - never thought about that.

Do you know if putting on longer blades also have the same non-linear effect on power?

[gwright]

I don't know. Longer is definately more efficient, as I've seen many times with planes (larger, slower turning props with the same input power are more efficent), but I don't know how you'd calculate any delta. Of course if you just bolt on longer blades and try to spin them the same rpms, you're just wasting a lot more power than you need to.

Hey,.. maybe we can strap 5 foot blades on a logo 10 and hover it at 10 watts per pound!! <G>

[BobbySmith]

Hey yea really good stuff Gary!

[JKos]

> And this is why you want VStabi/CSM/Flybarless.. you can lower headspeed and
> keep cyclic rate You gain alot.

Bingo.

> Do you know if putting on longer blades also have the same non-linear effect on
> power?

I have visions in my head of a test rig for collecting data to answer these questions. The required test rig is actually rather simple. All you have to be able to measure is the torque required to spin a given set of blades at a given RPM. If you know the torque and RPM, you know the power!

The torque measurement would be independent of the drive system used so one doesn't have to worry at all about its overall efficiency. I would like to collect data for producing various amounts of lift at various headspeeds.

Now, if I could just turn those visions into action and real hardware... I'm slowly collecting blades to do the tests with (currently have Mikado wood 500, Mikado fiberglass 500, Mikado CF 500, TT CF 550, Radix 600, SAB 690 and SAB 710) and have the power system to spin any of those to sufficient headspeeds.

- John

[MrMel]

I think its just to turn to E-airplane guys, they know this probably.
Since its exactly their way, running a prop at a certain pitch, then changing prop-size to bigger/smaller etc.

[JKos]

MrMel,
Yeah, we should be able to gleam some info from them. But I want to get real data for our blades. I would love to test a bunch of different blades and build graphs of the results for comparison purposes. It would apply equally to electric or nitro.

- John

[MrMel]

Yeah it would be nice, I switched from 690 to 710 on my E-Raptor the other day, total flight-time stayed about the same, but peak watts went though the roof.


Edit: with through the roof I mean 95amps/4000 watts from my A123 batts (42C), and they still going strong.

[misskimo]

hey , yeh! I do agree with this, great work Gary , I bet I know who your smart good friend is , Starys with a C, YEH! :smokin: :noteworthy

[n808]

It can be said that the increased revs will require less pitch, which is true, but load difference from the tiny pitch change is minuscule compared to the load increase of rpms so it's virtually irrelevant.
Interesting and accurate numbers in theory, but I do not completely agree with the statement above. I believe the difference in pitch resulting from say a change from 3000 to 2000 rpm affects the torque, and thus power/current requirements enough to affect the numbers measurably. After all, the same amount of lift has to be generated to keep the helicopter in the air.

[0636]

I've checked my FDR stats for Trex 450 and 600. The resulting formula more looks like this:

(High rpm / Low rpm )^2 = High Amp / Low Amp

So it's a SQUARE not a CUBE relations.

Examples:

Trex 600 hovers:
at 1850 rpm with 24A
at 2000 rpm with 28A

(2000/1850)^2 = 28 / 24

Trex 450:
2950 rpm - 16A
2650 rpm - 13A

(2950/2650)^2 = 16 / 13

[greg006]

an eagle tree logger will verify this, very interesing as losses due to ineffeciency are always there.

[greg006]

forgot to mention, the new downloaded magazine from readyheli has a dyno type of set up using an eagle tree logger, this gives amazing insight of a helis performance under load