Mavic Battery and Speed efficiency chart

[dwallersv]

Due to the Mavic's shape, the extra lift it generates at faster speeds balances out with the extra power it needs to go that faster speed, leaving in its wake the net effect of a shortened trip, which significantly reduces total power required, thus for the same battery, increases total range.

This is exactly backwards, Adiru.

Because quads have to pitch forward to generate a forward vector, the attack angle of the lifting body of he Mavic shape results in an additional downward force added to the weight of the aircraft, requiring more thrust to maintain altitude.

Think of the body like a wing surface (the arms are irrelevant for this concern). As air hits the top of the aircraft because it's angled forward, it's deflected upward, resulting in a downward force on the aircraft (Newton's First Law).

 

[dwallersv]

Guys, this is all pretty vanilla aerodynamics. The same physics principles apply as for any aircraft: Thrust balances drag => constant speed, lift balances weight=> constant altitude.

In the case of a quad, energy is being used directly for both lift and forward thrust as the single thrust vector from each prop.

The reason there is an optimal speed for distance efficiency is for two reasons:

1) Energy is being used to simply maintain altitude. Because of this, at very low speeds energy consumption is distance inefficient -- most of the energy is being consumed hovering. Obviously the degenerate case -- simply hovering without moving for the entire battery -- is most inefficient in terms of distance traveled per unit Ah consumed... ZERO. So obviously efficiency increases as you go faster -- you'll end up with a higher efficiency figure for ft/Ah running an entire battery moving along at 0.025mph; even better at 1mph; 2mph; and on and on. All of these runs would take about the same time, because the energy going into horizontal translation is trivial -- all of it's essentially going into hovering.

If you gather a ton of experimental data doing careful runs incrementing 1mph each time, you'd find that at first the increase in efficiency vs. speed would be linear, up to the point thrust going to forward motion was below 3 or 4 percent. At that point, more and more thrust is going to forward motion in addition to what's being consumed hovering, so the curve starts to bend toward flattening as speed increases.

2) Air resistance (drag) increases as the square of speed. Because of this, the curve starts to bend downward, with efficiency actually decreasing with higher speed. This is because to go twice as fast requires 4x the forward thrust to overcome the increased by squared drag. Obviously, at very low speed changes (1 mph to 2mph) the double of drag (from 0.1oz to 0.2oz) is completely inconsequential compared to the total forces the aircraft is countering with thrust -- basically the weight of the aircraft.

Now, lets go 15mph. Drag is 2lbs. double to 30mph, now drag is 4lbs. A lot more power (energy/time) is needed to push against this drag.

The knee of the curve -- the point of peak efficiency -- will not be at the aircraft's maximum speed, because aircraft always have much more power than just that necessary to fly at peak efficiency -- it's a necessary safety margin.

 

[dwallersv]

Helicopter power vs speed...same principles as Mavic (discounting any "lifting body" effects)...in the chart, it's apparent that between about 40 and 80 mph, the total curve is pretty flat...which equates to the Mavic's curve between about 20 and 40. If the Mavic could go faster than 40, it's certain that it's curve would start to rise, just like the helicopter, due to wind resistance.

Any differences in the shapes of the helicopter curve vs the Mavic's curve are probably due to the ability or inability to measure more accurately (or again, perhaps because of other factors, like, perhaps, the "lifting body" effect):

Yes, that's the key.

Where the minimum on the power curve is for a rotary-wing aircraft depends on the shape.

It's all about drag, as the other force being balanced is fixed for the most part (weight).

 

[doccy]

What we need to know is... we are far out. Realise we need to get home sooner than we thought and worried about our battery.

On balance.... are we best to hit sport mode and go full throttle back.... or try and nurse it back with obstacle avoidance off in P mode?

Have the distance pros come to a conclusion? Which is safest?

 

[200V]

Pardon the rough 3D model, but here are some approximations at 20mph, 16 degree angle of attack (AOA). 20mph is pretty slow, so no real high/low pressure areas. This is assuming the blades are at enough speed to represent a solid disk (2mm thick).
View media item 932View media item 931View media item 930View media item 929View media item 928View media item 927View media item 926

 

[Cerberus]

Holy.. you guys really go in-depth pro like into this discussion..

kudos to you all

 

[200V]

At 40mph and 25 degree angle of attack. Now we see higher pressure areas (red), and a large low pressure area below the body (blue) - not the best setup for cooling the fins under the electronics.



3rd view is from rear, above
0.001 MPa = 0.145 psi , so the pressure differences shown are very small

 

[quick_dry]

great CFD!

How does it change if you remove the prop discs?

(or even matter if the fins weren't at their limit for heat transfer already - or although there is a reduction in pressure, is there an increase in mass flow? Either way, we're not flying at very high speeds) The body is a tube, and 25 degree AoA would still have a direct path into the entry behind the gimbal. A temperature log would tell the story.

 

[BadRad]

I agree with all ... well done science project (spoken as a former science fair winner myself). I hope he got a blue ribbon for this one ... But in any case he obviously contributed USEFUL information to others .... I've read about low & slow, but I think this data point approach is far more compelling. Who know what it will lead ya'll to?

 

[TTFullTimer]

While the model for drag and flow looks wonderful, there is no empirical data to validate the model. And for this thread, not a single prediction of battery usage per unit distance. Good exercise for the modeler.

 

[alex_markov]

I just did 3 test flights, same weather same start/end point, same hight ~10-15 m, nearly same route
Summary:
1) 66-68 km/h (Sport mode) - total flight 9.7 кm - 18% remaining battery or 8.45% battery discharge per km
2) 50 km/h (Р - mode, VAS Off) 12.15 кm - 28% start at 97% or 5.68% battery discharge per km
3) 32-34 km/h (Р - mode) 7.2 кm. - 54% or 6.39% battery discharge per km

 

[TTFullTimer]

I just did 3 test flights, same weather same start/end point, same hight ~10-15 m, nearly same route
Summary:
1) 66-68 km/h (Sport mode) - total flight 9.7 кm - 18% remaining battery or 8.45% battery discharge per km
2) 50 km/h (Р - mode, VAS Off) 12.15 кm - 28% start at 97% or 5.68% battery discharge per km
3) 32-34 km/h (Р - mode) 7.2 кm. - 54% or 6.39% battery discharge per km

So your best speed for your conditions was the same as the long rangers say about 32 mph or 50 kph. Thank you for reporting, I am sure it will help all of us if we have some difficulty and must return home using the least amount of our precious battery reserve. Click into sport mode and hold 50 metric or 32 imperial. I for one will remember that. Though for me I always have lots of battery left. I do not make long runs.

 

[alex_markov]

So your best speed for your conditions was the same as the long rangers say about 32 mph or 50 kph. Thank you for reporting, I am sure it will help all of us if we have some difficulty and must return home using the least amount of our precious battery reserve. Click into sport mode and hold 50 metric or 32 imperial. I for one will remember that. Though for me I always have lots of battery left. I do not make long runs.

Thank You,
It is a lot easier to disable VAS and fly full throttle in P mode then go to sport and try to maintain around 50 - sticks are better kept in 100% on long flights - easy for hands

 

[ICHOTT]

Fabulous article and great detail, as one said we just need to know the best way to get home so....
Is there a way program in RTH the return speed eh 32mph/50kph?

 

[ebaldestein]

My son did a middle school science project using the Mavic. See the attached graph. He (and I) expected a different result. I believe the results very clearly show that at 20 MPH and up to max speed, the battery use per foot traveled is equivalent. Therefore, there is no battery penalty for "coming home" fast (e.g. in sport mode) vs. slower. And, as has been discussed previously, below 20 MPH, you will actually use more battery per foot traveled. The "age old" question of the most efficient speed has been answered - it is 20 MPH or higher. View attachment 12817

So if I want to do a long distance journey should I do it in P or S mode?

 

[bjohnson]

Yesterday I flew 2 10000 feet flights the first full speed in p mode the second at full speed in sports mode in the sports mode flight I came home with 25 percent battery in p mode 38 percent. I got several high wind velocity warnings. I think the sweet speed for distance in about 20 mph.

No need, in the context of the mavic, faster is always better.

 

[bjohnson]

So if I want to do a long distance journey should I do it in P or S mode?

P mode at full speed

 

[bjohnson]

P mode at full speed

 

[bjohnson]

/* 1) 66-68 km/h (Sport mode) - total flight 9.7 кm - 18% remaining battery or 8.45% battery discharge per km
2) 50 km/h (Р - mode, VAS Off) 12.15 кm - 28% start at 97% or 5.68% battery discharge per km
3) 32-34 km/h (Р - mode) 7.2 кm. - 54% or 6.39% battery discharge per km */

Based on just these 3 data points, approximating the power curve with a 2nd degree polynomial and obtaining P(V)/P'(V) function, here are the results for flying for max ground distance:

View attachment 21611

1. In no wind, the most efficient speed to fly is approx. 43km/h, or 27mph.
2. In 40km/h (25mph) headwind, the most efficient airspeed to fly is approx. 64km/h, or 40mph; the groundspeed is approx. 24km/h or 15mph.
3. In 40km/h (25mph) tailwind, the most efficient airspeed to fly is approx. 39km/h, or 25mph; the groundspeed is approx. 79km/h or 50mph.
4. Other windspeeds - DIY

Of course, results may change if more detailed experimental data of power curve P(V) becomes available and the fitting function changes. This analysis is based on only 3 data points above.

/done

Th

 

[bjohnson]

Th

Th

Thanks for that great response. I can confirm from my experiments on long distance flights that sports mode top speed eats the battery and my best results have been in p mode full throttle usually 28 mph. Great to see the science behind it.