How long will a battery last based on these numbers

Hi I asked this question on SU but seemed to have gotten into a bit of trouble, I was referenced here.

I am getting into doing hardware build based on things like microcontrollers and microprocessors.

I am curious how to calculate how long a battery can power a certain object.

Let's say we have a motor that says something like

3.5V and 100W


I don't have a motor yet a search lead me to this one: AmpFlow G43-500 Motor

The big G43-500 motors work great for applications that require sustained power output of up to 500 Watts (0.67 horsepower).

Specs
Watts - Continuous  500
Diameter    4.3 in.
Length  5.3 in.
Efficiency  80%
Output Shaft    11-Tooth #25 Sprocket
Weight  8.6 lb
The above specifications are for 24V. The motors can also be used at 12V or 18V. The RPM is proportional to the voltage so running at 12V will result in half the no-load RPM that is shown above for 24V. The lower voltage also reduces the maximum achievable torque by 50%. The motors have also been tested and used at higher voltages resulting in higher RPM, torque, and power. Shorter duty-cycles are recommended for higher voltages to allow the motors time to cool.


I also saw these specs on another site

Model                G43-500
Watts - Continuous   500
Diameter (inches)    4.3
Length (inches)      5.3
Efficiency           80%
Voltage*             24*
Output Shaft         Sprocket

• The above specifications are for 24V. The motors can also be used at 12V or 18V. The RPM is proportional to the voltage so running at 12V will result in half the no-load RPM that is shown above for 24V. The lower voltage also reduces the maximum achievable torque by 50%. The motors have also been tested and used at higher voltages resulting in higher RPM, torque, and power. Shorter duty-cycles are recommended for higher voltages to allow the motors time to cool.

or something like that, how can I then say okay I have a 3.5 Volt 1000mAh battery

How long should it last?

If there's a formula that I can follow that would help. I am not trained EE.

• [EDIT]
• I want to thank David Schwartz for actually providing a good information to help clarify what I needed to then go do further research and learn the math behind all of this. I'd like to add this tutorial on how to calculate how much batteries you will need.
• I didn't go to school for engineering so this is all new to me.
• Have read through the dozens of "how long will my battery last" questions here? – PlasmaHH Feb 25 '15 at 13:17
• Based on your comments, I suggest doing a search for "quadcopter batteries" - you will get lots of pertinent information. – Andrew Morton Feb 25 '15 at 21:47
• If you're building a quadcopter, you don't want to run 24v motors from 12v. You need all the power to weight you can get, so you need to run them at 24v, maybe even a bit more if you're feeling lucky. – Neil_UK Nov 25 '16 at 11:20

A 3.5 Volt, 1000 mAh battery can supply 3.5 watt hours. That means the battery can supply 500 watts for 0.007 hours. So, with perfect efficiency of all circuitry, including stepping up the battery's 3.5 volts to the 12-24V the motor needs, you could theoretically supply full power to the motor for 25 seconds.

Of course, it's very unlikely the battery could tolerate being drained in 25 seconds. The fastest draining batteries I've seen can tolerate being fully drained in 72 seconds with only moderate loss of lifespan.

You're going to have to design a circuit to step up the 3.5 volts from the battery to at least the 12V that seems to be the motor's minimum specification.

An 11.1V 30-60C LiPO battery (such as those used for drones) seems like a reasonable match for your application, and could probably run the motor at 1/2 voltage (just under 12V) and 1/2 duty (pulsed). The one I linked to stores about 24 watt hours and could probably run the motor at 1/3 speed or so for about 5 minutes. It's designed to tolerate complete discharge from a fully charged state in as little as one minute.

Update: Since this is a quadcopter application, you should be looking at using a brushless motor with an electronic speed controller. Otherwise, it will be very difficult to adjust the rotation rate of the motor quickly enough to provide a stable platform. You should look at the design of a quadcopter that's similar in size and weight to your requirements and look at what batteries, motors, speed controllers, and props it uses.

• your almost right on the mark. I am interested in building a quadcopter. The initial numbers for the battery were just made up. Is there a formula or way to take a look at a series of parts, so say I have the numbers for the 12 volt motor from my original post and the 2200mAh battery from the link you provided. How can I calculate this motor will take x amount of time to drain this battery? – steffan Feb 25 '15 at 14:21
• Compute the number of watt hours the battery can hold (nominal voltage times amp-hour rating). Dividing the watt hours the battery can hold by the power the motor needs gives the theoretical number of hours the battery can run the motor continuously. – David Schwartz Feb 25 '15 at 21:01

There was a lot of babble in your question so it's not really clear, but you seem to be asking how long a 3.5 V 1 Ah batter will run a 24 V motor.

The answer, is no time at all in a practical application. The motor might be able to spin with 3.5 V applied and no load, but the torque will be so low as to be useless.

There are many types of motors and types of batteries out there. Find a combination that is properly matched. For example, you should be able to find 12 V motors that will run well from ordinary car batteries.

However, even this is premature. You first have to find out what the parameters are of whatever mechanical thing you are trying to drive with the motor. In particular, find how much power it takes. Power can be converted from one torque x speed combination to another with gears, but they can't change the overall power. You have to start with a motor that is sized for the load.

• I don't currently have the motor or the battery this was just a question to understand how this works. I am actually looking to build something like a quadcopter, I will need at least 4 motors as far as the size of those motors, the amps they use and the volts, watts, etc... I am currently unsure, that's why I am asking. After understanding how to calculate how long a battery of say 1000mAh can power a 12 volt motor then I can then calculate how many mAh I will need, etc. – steffan Feb 25 '15 at 14:18