# How to size a battery for a starter motor?

I am trying to size a battery for a starter motor for a 120cc 2-stroke engine. The starter is listed as 12V/250W (so 20A draw). The engine manufacturer offers a 3000mAh NIMH battery (so like ~30A max short-term current draw) with a 40A fuse.

How is it possible for that battery to start the motor? I thought that motors drew ~3x their rated power at start up?

Thanks!

• Not all motors do – PlasmaHH Sep 15 '18 at 20:47

The peak current drawn by a DC motor with a commutator is determined by the resistance of the armature winding. When the motor is first switched on, it will draw:

$$I = Vs/Ra$$

where $Vs$ is the supply voltage and $Ra$ is the resistance of the armature winding.

The current with the shaft turning is:

$$I = (Vs - Vb)/Ra$$

where $Vb$ is the back EMF generated by the speed of the armature.

$$Vb = Speed \cdot K$$

where $K$ is the volt per RPM rating of the motor.

The heat developed in the armature winding is $I^2 \cdot Ra$ so the higher $Ra$, the more internal heat is produced in the motor. That means an efficient motor needs to have a low $Ra$ value and a high initial starting current.

If the motor is 90% efficient, the initial current will be 10 times the normal running current. While it is impossible to determine the maximum starting current without knowing the design details, it could easily be 3X rated current and is likely to be much more than that.

The peak starting current is an instantaneous value. As the motor speed increases from standstill, the current drops quickly.

The above analysis neglects the internal resistance of the battery. That is likely to be important. However the more the current is limited by the battery, the longer it will take the motor to accelerate. It may be difficult to determine if a wrong choice of battery will prevent the engine from starting or harm the battery.

• @Misunderstood: I revised my answer. Ra, Vb and K are defined in the answer. X is multiplication. The mechanical details determine the cranking time but have no bearing on the peak motor current. – Charles Cowie Sep 16 '18 at 2:47
• @Charles - Hi, I've re-written your answer using MathJAX notation for the formulas, as I think that makes them easier to parse (especially by separating them from the text itself), and it removes the ambiguity of what "X" means (I used the maths notation of a central dot for multiplication; an alternative would be to replace \cdot by \times in the MathJAX). I hope that looks like an improvement to you. I have no problem if you dislike it and prefer to rollback to the previous version - it's your answer, I'm just trying to make it easier for those of us without your knowledge, to read it :-) – SamGibson Sep 16 '18 at 3:37
• @Misunderstood: SamGibson has kindly re-formatted my answer to make it more understandable. – Charles Cowie Sep 16 '18 at 10:10

I do not know specifically about your 3X rule of thumb but it may only apply to AC motors. You have to oversize an AC Motor to match the torque of a DC Motor.

Just because the starter motor is rated at 250W does not mean a 20 amp draw is required at 12V. The current draw is also related to torque. Or how many teeth on the starter vs. the number of teeth on flywheel.

Some Li-ion batteries can easily supply 10X their capacity i.e 3000 mAH.

Small engines start with little power required compared to a car or large motorcycle.

A battery for a 120cc engine is considered a powersports battery and Cold Cranking Amps is not applicable so they are not spec'd that way. When lead acid, powersports batteries are usually the same as a general purpose Sealed Lead Acid (SLA) rated only with capacity and maximum discharge rate measured in amps.

Most suggested replacement SLA batteries for a 120cc engine are around 4 AH.

There are many types of Li-ion chemistries. Most common 3000 mAH can withstand a 1C, 3 amp, continuous draw (e.g. LiCoC2 (LCO, Li-cobalt).
The Li-ion batteries use for power tools have a LiMn2O4 (LMO, Lithium Manganese Oxide) chemistry and can supply a continuous 10C (20 amp) and as much as 50 Amps for short periods of time.
See: Summary Table of Lithium-based Batteries