 # Voltage to Ah Relationship Question

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Assuming a vehicle is driven the same for both examples, I was curious about something...

Would each battery pack described below provide the same running time (again, given that both scenario's are run exactly the same way):

1) X Volts @ Y Ah
2) X*2 Volts @ Y/2 Ah

I understand the significant performance differences between the two, just looking to compare two exact same driving scenarios and see if I understand the situation.

Oz
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#### GerhardRP

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Assuming a vehicle is driven the same for both examples, I was curious about something...

Would each battery pack described below provide the same running time (again, given that both scenario's are run exactly the same way):

1) X Volts @ Y Ah
2) X*2 Volts @ Y/2 Ah

I understand the significant performance differences between the two, just looking to compare two exact same driving scenarios and see if I understand the situation.

Oz
Hi Oz, here is how I look at it.

#1. A modern controller is a DC power transformer with a variable voltage stepdown. The motor voltage equals the battery voltage times PWM%. The motor current equals the battery current divided by the same PWM%. The power out is equal to the power in minus maybe 2% inefficiency.

#2. Battery power loss due to internal resistance and loss of capacity from the Peukert effect are dependant only on the the total power delivered by the pack.

#3. It is possible to set up "two exact same driving scenarios" by setting the motor voltage limit in the controller to the value of X in your question. With this setup, everything is the same in both senarios with regard to battery power and motor power, so the two ranges and performances will be identical. The only difference is that resistive losses in the cableing, fuse(s) and contactor between the battery and the controller will be smaller in the high voltage case.

#4. The usual reason to go to higher voltages is to allow power to be delivered at higher RPM. Look at the second attachment in this post http://www.diyelectriccar.com/forums/showthread.php/dc-motor-theory-and-model-39931.html. Compare particularly the 75 and 150 volt curves. You can see that the power available at high RPMs is doubled giving seriously better "performance", but it comes at the expence of double the stress on the batteries resulting in greater internal power loss and Peukert capacity loss.

#5 Bottom line is you can trade range for performance, mainly through battery losses. Same way you trade operating speed for range through aero losses.

Gerhard

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