# Need help calculating the thrust on quadcopter motors

I'm trying to calculate the lifting capability of my four quadcopter motors. I tried using eCalc but it doesn't have battery I'm using. Are there any equations to keep in mind for doing these calculations? Here are some relevant details:

Battery: 2200mAh 3S 25~50C LiPo

ESC: 25A

Motor: 1240kV Brushless

Propeller: 8x4

Any help would be much appreciated, thanks!

• Are you asking about the thrust that the motors provide or the leftover lifting capacity after you consider the weight of the assembled vehicle?
– Ian
Mar 23 '14 at 19:12
• Thanks for clearing up the difference. I'm asking for both in that case. Mar 23 '14 at 20:58

You could probably calculate this value, but the sensible thing to do would be to just measure it directly.

Just turn it upside-down and put it on a kitchen scale as shown in this video. • This. Empirical testing for things like this almost always produces superior data because it's so hard to take everything relevant into account. As a bonus, it's also significantly faster! Jul 28 '15 at 17:52

Unfortunately, the basic equations for thrust aren't all that basic when you also want to look at things like motor efficiency, which is partly why all these quadcopter calculators are so popular. The one at http://www.drivecalc.de/ is pretty handy, especially if you want to define things like custom motors or batteries.

• About 0.053 N/W thrust efficiency for that prop
• About 260 Watts at the shaft for that size motor
• About 14 Newtons of thrust per motor
• 14 newtons will hold up about 1.4 kg
• Max weight for a static hover with 4 motors is about 5.6 kg
• You should probably be about half this for a quadcopter that flies well, so try to get its weight under 2.8 kg

If this is your first quad, I'd say that 2.8 kg (6.2 lb) is a little heavy. The bigger they are, the harder they fall. This adage is definitely true for quadcopters.

• ...as far as lifting capacity, I'd say add up all your components and see how far under 2.8 kg you are. Whatever is left over would be a good guess for a lifting capacity. Jul 25 '14 at 19:17

Here is the equation I was able to come up with:

THRUST (kg) = ((2.83 x 10-12) * (RPM^2) * (DIAMETER^4) * (((AIR DENSITY) * 23.936) / 29.92) * CF) / 2.2

where *RPM is motor kv multiplied by battery voltage *DIAMETER is total length of propellers *AIR DENSITY has to be looked up or calculated separately *CF changes based on prop type but should just be "1" for your calculations

Hope this helps

• Question. At first is it 2.83 * 10 - 12 or 2.83 *10^-12. I'm asking because it appears that you've wrote it in the first way i mentioned, which makes no sense because you could just calculate the result as there's no variable in this parenthesis. Tested it both ways. This equation gives me completely erroneous results. Aug 28 '15 at 14:16

There are way too many factors and unknowns that you would have to consider to simply calculate the thrust. The simplest way is to do it empirically - build a rig where you can simply weigh the motor, subtract its weight and start increasing rpm and measuring the thrust in steps and also current and voltage so that you can calculate efficiency. The most important factors that will impact the thrust and efficiency are: the type of the motor, the propeller pitch and diameter and the materials the propeller is made of and how well the motor and propeller are balanced. Generally the motors that have lower RPM/V (KV rating) and can run on higher voltages are more efficient because higher currents mean higher heat loss.

Keep in mind that even with the rig with the scale, your measurements won't be 100% representative because first of all the motors are attached to arms which create drag and energy loss due to non-zero stiffness and when you have several motors running in the same plane next to each other, they interfere and the actual thrust is slightly lower. The closer the tips of the propellers will be to each other, the less efficient it becomes. A recommended separation is at least 1/3 of the propeller diameter.