# Physics of the Amazon Octocopter Drone

Publié le 1 Février 2014

I, for one, welcome our Amazon drone overlords. There, I said it.

This seems crazy. The basic idea is that these little drone copters would carry small packages to nearby homes. What does physics have to say about this plan?

#### Gathering Data

What do we even know about these drones? Here are some things you could find if you watched this 60 Minutes interview with Jeff Bezos.

- This is not intended for all Amazon items.
- Around a 30 minute delivery time.
- The drone (Amazon Air Prime) will launch from distribution centers and have a range of about 10 miles (with the current version of the drone).
- The drone is an octocopter. This means that it has 8 tiny rotors. I’m not exactly sure of the size.
- The octocopter can carry a payload of about 5 pounds (2.3 kilograms).

That’s about all I got from the video. There is one other thing to estimate: the size. I’m just going to totally guess that the yellow package box is 10 inches long. If this is the case, then each rotor has a radius of about 0.12 meters and the base of the octocopter is about 0.88 meters long. If I just look at the “control” part of the octocopter, it perhaps has dimensions of 0.44 x 0.44 x 0.1 meters.

#### The Physics of Helicopters

I don’t want to go into all the details again so here is an older posts where I model the physics of flying helicopter (with the S.H.I.E.L.D. Helicarrier). The basic idea is that a helicopter (or octocopter) flies by pushing air down. When the helicopter pushes air down, it creates upward thrust. When the thrust is equal to the weight, the helicopter hovers.

What about power? If a helicopter has very large rotors then it can push down more air and the speed of air doesn’t have to be that great. For a smaller rotor helicopter with the same mass to fly, it would have to push down air at a greater speed. Speed is important since it requires more power to push air at a faster speed.

In the end, I get an expression like this:

Just to be clear, I used the following variables:

- P = power in watts (this is the power to hover assuming 100% efficiency).
- ρ = density of air (at sea level, this is about 1.2 kg/m3).
- m = mass of helicopter plus payload.
- g = local gravitational field (9.8 N/kg).
- A = rotor area.

Looks crazy, but it mostly agrees with actual data from real helicopters. I am probably off by a bit, but I am going to use this anyway – for estimates.

#### Estimating the Power of Amazon Prime Air

What kind of battery would this octocopter need? How long would it last? Let’s make some estimates.

All I really need is the total mass and the rotor size. If we start with the rotor size, that’s not so difficult. Assume 8 rotors with a radius of 0.12 meters, that would give a total rotor area of:

What about the mass? If the thing can carry a 5 pound payload, maybe the octocopter itself is 10 pounds (I think this is a low estimate). This would put the payload plus vehicle mass at 6.8 kg. Plugging this into the equation above, I get a required flying power of 548 watts. That’s a bit higher than I expected. Also, let me point out that this would be a hovering power estimate. Clearly, it would require more power to fly horizontally also. Actually, that might not be true – I’m not an actual helicopter pilot, so I’m just guessing.

**How about a battery?** If I want to calculate the energy stored in a battery, I need to find the total energy required. Jeff Bezos said that the delivery would be under 30 minutes, but how much of that time would be spent flying? If it was traveling over a 10 mile journey, that would have to fly fairly fast to get there in under 30 minutes (assuming it takes at least 10 minutes to get the package ready). That would put the drone speed at about 30 mph. I would guess it be about half that speed. Of course the speed doesn’t matter as much as the time. Let me just guess that the octocopter will need to fly for 30 minutes minimum.

Using this time, I can calculate the required energy stored in the battery:

Now to pick a battery. The lithium-ion battery seems to be a popular choice with things like this. According to Wikipedia, it has an energy density of up to 0.875 MJ/kg. How massive of a battery would this octocopter need? For 9.86 x 105 Joules, the battery would have to be 1.13 kg. Of course this also assumes everything is 100% efficient. What if I bump the battery mass up to 2 kg? That would leave 3.5 kg of octocopter mass for things like motors and controllers and a GPS. I guess that’s possible.

This is of course, just an estimate. However, even with these “best-case” scenarios it seems like Amazon could get this to work. Well, they certainly can. The octocopters in the video are probably real. It can work, but would it be practical?

#### Other Thoughts

My first thought when seeing this delivery drone was: this would be perfect for pizza delivery. Maybe this is a sign that Amazon is going to get into the pizza delivery business. Really, it could work for any type of food delivery. What about a beer? That would be perfect.

Everyone thinks this octocopter would be a problem with the FAA. I tend to agree. I just have a hard time picturing the FAA approving something like this. Here are some other thoughts.

- Would people try to shoot these out of the sky? Surely, some fool would. It would still be theft (even if a pizza was stolen) and it would still be illegal. I guess it would be easy get an alert if one of the drones went down.
- What about weather? I can see it now. “Your Amazon Prime Air shipment has been delayed due to weather”.
- Let’s say the thing can run for 30 minutes on one battery. Now it will need to be charged. That doesn’t seem very practical.
- Suppose a drone makes a delivery to some kid waiting for something important. The kid acts like a child and runs out to get the delivery. Oh but wait. Spinning blades…. Or what if my dog attacked the octocopter? Would each house need a special Amazon Prime Air landing pad?
- If Amazon can make these things, why can’t everyone else? Perhaps the skies will be buzzing with drones from different companies. Maybe drones could take out drones as a form of competitive business.

I will leave you with just one question to consider. What if Amazon wanted to deliver 10% of their products via drone. How many drones would they need on hand? Yes, you will have to make some wild estimations here. Don’t let that stop you. Clearly it never stops me.

About :

**Rhett Allain** is an **Associate Professor of Physics at Southeastern Louisiana University**. He enjoys teaching and talking about physics. Sometimes he takes things apart and can't put them back together.

Read more : http://www.wired.com/wiredscience/2013/12/physics-of-the-amazon-prime-air-drone/