# How to maximize your practical lift/weight ratio in a multirotor?

My friend and I are currently working together in a multirotor competition. He's an experienced flyer and I'm more of a numbers guy (though my background is in software engineering, not aviation).

Our latest challenge involves maximizing our Lift to Weight ratio. Essentially, we're going to measure how much our craft can lift and divide that by our craft's weight.

My preliminary research seems to show that the most obvious way of doing this is by adding more motors+props to the craft. So, we're considering building a bare-bones dodeca-copter.

This seems like a very simple approach... maybe too simple. I'm worried that although it's very intuitive it may also be very naive.

So, I ask the community, is our approach sound? Are we missing some common optimizations that could help us?

In other words: How to maximize your practical lift/weight ratio in a multirotor?

# Update

We've been able to find more powerful motors (E800 instead of E310). We have fewer of them, but I think we're still better off with them. Here's the the breakdown of our build:

• Main components (Flight controller, receiver, nuts, screws) = 313g
• We're using E800 motors
• Unit weight: 106g
• Unit lift: 2100g
• ESC weight = 44g
• Prop weight = 14g
• Battery weights = {410g, 584g}

The only frame material we have access to right now is square aluminium tubing. Each "bar" of tubing weighs about 88g.

I did some calculations for a few different setups and this is what I got:

## 4 motors, 4 arms

This configuration requires 1.5 "bars" of frame materials. This gives me the following total weight:

(4 * (motorWeight + EscWeight + PropWeight)) + (frameWeight) + batteryWeight + MainComponentsWeight
(4 * (106g + 44g + 14g)) + (1.5 * 88g) + 410g + 313g
= 1511g


The total lift is 4 * 2100g = 8400g which gives us a L/W ratio of

8400g / 1511g = 5.56


## 6 motors, 6 arms

This configuration requires 4 "bars" of frame materials. This gives me the following total weight:

(6 * (motorWeight + EscWeight + PropWeight)) + (frameWeight) + batteryWeight + MainComponentsWeight
(6 * (106g + 44g + 14g)) + (4 * 88g) + 410g + 313g
= 2059g


The total lift is 6 * 2100g = 12600g which gives us a L/W ratio of

12600g / 2059g = 6.12


## 8 motors, 4 arms

This configuration requires 4 "bars" of frame materials but has two motors mounted per arm. This gives me the following total weight:

(8 * (motorWeight + EscWeight + PropWeight)) + (frameWeight) + batteryWeight + MainComponentsWeight
(8 * (106g + 44g + 14g)) + (4 * 88g) + 584g + 313g
= 2561g


The total lift is 8 * 2100g = 16800g which gives us a L/W ratio of

16800g / 2561g = 6.56


## Conclusion

If I'm doing my calculations correctly then it seems that our best option, given our limited resources, is an octocopter on 4 arms.

I'm not all that surprised since this configuration has the highest %age of total weight associated with motors.

Is 6.56 a decent Lift to Weight ratio? Is there anything else we can do to improve it?

# Competition Results

Weigh-in: 2460 Lift (meters of rope): 34m @ 346g/m Lift (grams): 11764g

Lift/Weight ratio (excluding craft): 4.78

Lift/Weight ratio (including craft): 5.78

So, all in all, not too far off from our "ideal" prediction.

• By adding motor+propeller+battery assemblies of the same L/W ratio, you indeed reduce the payload portion that each assembly has to lift, so you can lift more. The limit is when the individual lift starts reducing due to the turbulence created by neighboring propellers. Related: Does the ARCA hoverboard violate known limits on small-diameter electric fans? – mins Sep 26 '16 at 11:40
• Yeah, that's what I was worried about. On paper our 8-motor 4-arm setup seems best, but the two motors per arm are insanely close to each other. My teammate tells me there isn't much power loss associated with this, but I'm sceptical. If we had more time I'd run practical tests with each setup. Unfortunately, we only have the time for one build. – MetaFight Sep 26 '16 at 18:38
• I'm not sure if this will help, just throwing out the idea that ducting the fans may help reduce the power loss by having the two props close together at the end of one arm. You will have the additional weight of the ducts, and will have to do some math/research to determine the best design for the ducts, but they may help. Not an aerospace engineer! – FreeMan Sep 27 '16 at 13:18
• Adding motors, and associated propellers, structure, and batteries (assuming the same endurance is needed) will increase the weight almost as fast as the lift, because the components you are adding are almost all the weight. In fact, you'll need to make the structure stronger and that means double size structure will weigh more than twice as much, leading to lower L/W for larger design. – Jan Hudec Sep 27 '16 at 21:59
• However, you have the "main components" that make rather large fraction of the total weight. If that's something you can't change and does not scale, you sure need a bigger craft. – Jan Hudec Sep 27 '16 at 22:07

To maximize lift, use the most powerful motors and let them turn the propellers at the highest possible speed. To minimize weight, make the structure as light as possible (use round carbon fiber/epoxy tubes instead of square aluminium ones, for example) and use only as much batteries as needed to achieve lift-off.

I would expect that there should be some more rules to ensure that the winning entry is actually useable. You did not mention any of this. Now efficiency comes into play, and the number of parameters to watch goes up. A lot.

• Make sure that your propellers act on as much air volume as possible. Let them run at a reduced speed for better efficiency. You need to test your particular engine-propeller combination where the sweet point is - there is no general number for best efficiency.
• Put as little drag in the way of the airstream as possible. This requires careful study of all shapes and cross sections. See on the right side of the picture below for a general overview of the drag coefficient of different 2D shapes.

Figure 33 from Sighard Hoerner's Fluid Dynamic Drag, Chapter 3.

As you can see, round is better than square. However, depending on the local Reynold number, it can help to add turbulators or local roughness to trip the boundary layer.

Also, adding motors to one arm will reduce the efficiency and thrust of the second propeller. Your 8 motors / 4 arm design will end in a disappointment - you cannot simply add the thrust of an individual motor-propeller combination once they interfere with another unit.

Without detailed knowledge of the rules of your competition, it is hard to give more detailed advice. I expect that a lot of educated trial and error will produce the best outcome.