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I frequently see oversimplified methods for calculating spinner weapon spinup time given on forums and social media sites. Builders constructing combat weapons based on these methods would be disappointed in the performance of the resulting system.
Q: A joule of kinetic energy is equal to a wattsecond of electrical output, so if I have a spinner weapon that stores 1200 joules of energy and I power it with a 400 watt brushless outrunner motor it should take I've written the following detailed explanation of the factors involved in estimating spinner weapon performance as a handy reference to which I can point interested builders. A: This would be true if your '400 watt brushless motor' actually produced 400 watts of output power over the full speed range from zero to maximum RPM needed to spinup a rotary weapon  but this is not the case. Some background:
Hobby brushless outrunner motors are typically intended for model aircraft use. They are often rated rated by their Maximum Continuous Power which relates to how large a propeller they can spin at full throttle without failing from thermal overload. This power level has the motor operating up high in its RPM range, close to the motor's peak efficiency. Spinning up a kinetic energy weapon on a combat robot places much different demands on a motor; a heavy load for a short period to bring the weapon up to speed but very little continuing load once it has reached top speed.
The Peak Power available from the motor is considerably greater than the Maximum Continuous Power, but can be maintained for only a short period without thermal damage to the motor. Peak power output is available when the load on the motor limits speed to 1/2 the unloaded motor RPM  see chart below. The power available from the motor at the high and low ends of the RPM range is much less than peak power. The average power available to spin up the weapon as the motor climbs from a dead stop to full speed is only a fraction of the 'peak power'.
I'll use the PropDrive 2826 1000KV Brushless Outrunner Motor as an example. The motor is rated 235 watts continuous output on a 4cell LiPo battery and has a stator resistance of 0.140 ohm. The estimated 'peak' power output is very close to 400 watts:
Peak Output Watts
Using the PropDrive 2826 motor with a 2:1 belt reduction to spin a steel weapon bar 41mm x 12mm x 240mm (0.0045 kgm^{2} Moment of Inertia) to 7,000 RPM (95% of peak motor RPM) gives very close to 1200 joules of stored kinetic energy.
= Voltage^{2} ÷ Resistance × 0.25 = 15 × 15 ÷ 0.14 = ~400 Watts
OK, how do you track the effect of these fluctuating power levels to find out how long it takes to spin up the weapon? I've written a pair of tools to do the calculations for you! Your choice of a sophisticated Excel spreadsheet or a simplified online javascript calculator: Click Here.
Q: Wait... What's that formula you used to calculate Peak Output Watts? Where did that come from? A: At stall a Permanent Magnet Direct Current (PMDC) motor produces maximum torque and will consume:
Power Consumption at Stall (Watts)
The mechanical power output of a motor is a product of torque and RPM. At stall, a PMDC motor produces zero mechanical power: the torque is at maximum but RPM is zero. PMDC motor torque and amperage consumption decrease linearly to approach zero at noload RPM ^{1}. At maximum noload RPM the motor again produces zero mechanical power: the RPM is at maximum, but the torque is zero.
The product of torque and RPM is power, and power reaches maximum at 50% of the noload RPM where the motor will consume very close to 50% of the stall amperage:
Power Consumption at Peak Output (Watts)
The efficiency of a PMDC motor in converting electrical power to mechanical power varies with motor design, materials, and RPM. Approximately 50% efficiency at peak output is typical. This gives an estimate of power output as:
= Voltage × (50% of Stall Amperage)
Peak Output (Watts) = Voltage × (50% of Stall Amperage) × (50% Efficiency)
The above equation simplifies to the equation I use to estimate peak motor output power:
Peak Output (Watts)
Brushless motors do not specify a stall amperage figure because it is the brushless motor controller that determines current flow at low motor speeds. However, brushless motor specs do commonly provide a Terminal Resistance that allows you to calculate a theoretical stall amperage:
= Voltage × Stall Amperage × 0.25
Stall Amperage
A little algebraic substitution combines the two equations above to provide a onestep shortcut that estimates peak output power from just voltage and terminal resistance:
= Voltage ÷ Terminal Resistance
Peak Output (Watts)
= (Voltage^{2} ÷ Terminal Resistance) × 0.25 Need more info? There are more than 580 questions and answers in the Ask Aaron combat robot motors and controllers archive:
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