Flight time/battery life

The Santa Cruz project will take a lot of flying time, so I'm trying to maximize that.  I have looked at several posts about how to increase that time.

Some websites claim that to get maximum airtime, the weight of the batteries should be half the weight of the craft.  Others have similar answers. 

I disagree with most all of them!  I think I know how they arrived at their answer, but it is just plain wrong.

The efficiency of a propeller/motor combination is not linear at all.  At a low RPM and light load, the efficiency is good, but at heavier loads, that isn't the case. To get long airtime, you need all the efficiency you can get.  You have a certain weight, and you need to keep the number of Watts consumed at the lowest possible level.

For example:  Using a Turnigy 3536 motor (910KV) spinning a 12 X 5.5" APC prop and powered with a 4 Cell LiPO, I get 1KG of lift when the motor is consuming 173 Watts (5.78g/Watt) .  But when I increase the speed of the motor to max, the lift is 1.8Kg while consuming 450 Watts (4g/Watt). Note that I did not account for any losses in the ESC or wiring.

When I use the same motor and spin a 11 X 4.5 prop, to get 1Kg of lift, the motor consumes 184 Watts (5.43g/Watt), at full RPM, I get 1.5Kg of lift while consuming 284W (5.28g/Watt).  The decrease in efficiency isn't so dramatic with the smaller prop because the smaller prop can't get to the 1.8Kg level that the 12" prop managed.

Consider a battery that I just bought:  A Turnigy 4 cell 10Amp/hour (10,000mA/hour) battery.  It weighs 820g.  If we assume that the battery averages 15.5V during its discharge cycle, then the energy in the battery is 10 X 15.5 = 155 Watt/Hours. If my motor and my props and the rest of my aircraft weighed ZERO grams, and using the example above, one 12" prop/motor combination would consume 820/5.78g = 141 Watts.  My battery has a capacity of 155 Watt/Hours, so with a 141 Watt draw, the prop could hold it in the air for 155/141 = 1.09 hours = 66 minutes.  Not bad.   But wait!  We have not accounted for any weight except the battery. 

The motor weighs 105 grams and the propeller weighs 20 grams.  The speed controller weighs 25 grams and 2' of 14GA wire weighs 30 g.   That is 180g total.  Since we can lift 5.78g/W and we just added 180g, we now need 31 more Watts to lift those items.  141 Watts + 31 Watts = 172W, and we are very close to 1Kg total weight.  At the 172W level, we can stay in the air for 155/172 = 54 minutes.

So far, we have added no airframe, no flight controller, no camera, no landing gear, no ....

Also, we are producing only as much lift as we have weight.  We are hovering, not going up,or sideways.  If we have to do those things, we will be consuming much more power.  You might think that going sideways is not much harder than hovering.  Think again!  if you are flying at a 45 degree angle, half the motor thrust is (effectively) going sideways, while half is going down.  It now takes twice as much thrust to hold altitude as it does when hovering.  And you may wish to climb.  That will take more power than hovering as well.

So kudos to those who have obtained more than 1 hour of hovering flight.  Their airframe was toothpicks, and their batteries were special.

Adding batteries doesn't always help, since my measurements show that propeller/motor efficiency drops as they get loaded more heavily.  What good is twice the power if the efficiency is only half as much?

The secret is that larger propellers and motors, spinning slowly are not only efficient at light loads, their efficiency doesn't drop off until the load gets quite heavy.  So if you have a lot of batteries, you can lift them efficiently only if you have big motors and big propellers. You might think that such an arrangement would be good even for small craft, but you would be wrong since the larger motors and larger propellers weigh more.  The fact that the propellers are larger means that the airframe must also be larger and heavier.

So, if you like airtime, get the lightest frame you can find. Use big propellers (like 16") and big motors that have a rating of no more than about 510KV if you are using a 4 Cell battery or 380KV if you are using a 6 Cell battery. Keep weight to an absolute minimum, and it shouldn't be too hard to stay in the air for more than 30 minutes - as long as you aren't doing any stunt flying.