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#### zaraf

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Dear community,

I am a beginner and trying to calculate the starting torque for my vehicle project with following specs:
Vehicle mass (with passengers and battery)=1000kg
Motor selection= AC-20 HPEVS depending on the starting torque i calculate

I need to meet the following performance criteria:

1. 0-60kmh in 20 Seconds
2. Vehicle to be driven in urban city traffic like paris, tokyo etc.

Based on this information I have tried to calculate the starting torque needed:

Acceleration from 0-60kmh in ms2 = 0.553
Mass kg =1000

Accelerating force= ma= 553N
Force against rolling R= u m g = 0.01 * 1000*10= 100N

Total tractive force= 653N

Now if this is the force needed to move the car, I want to reverse engineer to get to "motors torque":

Wheel torque = Tractive force * radius tyre in m = 653 * 0.3 = 195Nm

Now it is known that the Motor torque= Wheel torque / Diff Ratio

so assuming a Diff Ratio of 5:1,

a Motor torque= 39 Nm continuous is what I need?

My question:
1. Is this calculation correct and realistic for selecting a motor for my criteria?
2. Which graph should i refer to Torque vs RPM in "Peak" or "Continuous"?

#### Duncan

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6,613 Posts
Hi Zaraf
Think about your torque - ask yourself what will happen if you stop and have to then climb a speedbump or a curb

That is probably a more reasonable minimum torque

#### PStechPaul

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I used my http://enginuitysystems.com/EVCalculator.htm to do the calculations.

I come up with 0.833 m/s^2 for the acceleration, and a force (thrust) of 1082 newtons. For wheels 600mm diameter, wheel speed is 531 RPM at 60 km/h. Power required to maintain this speed is 18 kW or 24 HP. If the motor is running at 3000 RPM the drive train ratio would be 5.6 and motor torque is 57 N-m or 42 lb-ft. A ratio of 5:1 would be a motor speed of 2655 RPM and motor torque of 64 N-m or 47.5 lb-ft.

#### dcb

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1. Is this calculation correct and realistic for selecting a motor for my criteria?
Not sure on the math, but realistically you need to account for hills and air resistance and rolling resistance and wind/etc.

2. Which graph should i refer to Torque vs RPM in "Peak" or "Continuous"?
With all the above variables in mind, typically peak is used for brief acceleration and brief hill climbing, whereas continuous is the max you want to sustain (i.e. continuous top speed with minimal wind/hills/etc).

#### kennybobby

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Howdy Paul,

Is it possible to change the incline angle on your calculator--it didn't seem to let me input a different angle.

edit: it was way too early to be doing math before coffee...Major's math is better than mine, 1082 Newtons/4.4 is about 234 lbs thrust...my bad Paul, sorry for the confusion.

#### major

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1082 N = 243.2 lbf.

IMMIC

major

#### PStechPaul

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Howdy Paul,

Is it possible to change the incline angle on your calculator--it didn't seem to let me input a different angle.
The angle and % slope are calculated from the acceleration. 0.98 m/s/s is 1/10 G. That comes to 5.739 degrees or 10% slope. 9.8 m/s/s is 1 G which is 90 degrees, and percent slope is essentially infinite. I think that is correct; at least it corresponds to the following calculator:

http://www.calcunation.com/calculator/slope-percent-conversion.php

A 100% slope is 45 degrees, where the vertical rise is equal to the horizontal run. I think it would be more logical to use the hypotenuse as the run, in which case 45 degrees would be 70.7% and 90 degrees would be 100%. Another way to define slope would be by percentage of angle to 90 degrees. Thus a 45 degree angle would be 50%.

The values for the calculator are for a single speed or without a transmission. It should be possible to accelerate much faster (or climb steeper slopes) with a transmission. To do that, you might try something like a 11.3:1 ratio and a speed of 30 km/h. I found that you can get an acceleration of 2m/sec/sec with 24.7 HP, and 3000 RPM at 30 m/sec. This would take 8.3/2 = 4.16 seconds. Then you could shift to the 5.6:1 ratio for the previously calculated 0.83 m/s/s with the same 24 HP, so you would reach 60 km/sec in an additional 8.3/0.83 = 10 seconds, and total 0-60 km/h in 14.16 seconds (ignoring time to shift).

A more important factor favoring a transmission is negotiating occasional steep slopes, such as driveways and ramps. A 30% slope is 2.83 m/s/s and 24.6 HP at 1500 RPM requires a 34:1 gear ratio. The fixed 5.6:1 ratio and a speed of 5 km/h results in a motor speed of 250 RPM and torque of 117 lb-ft. But for a motor with nominal speed of 1800 RPM, that would require a 40 HP motor. Since a motor can run at 2x for a short time, the 24 HP motor will be adequate. But if it is a 3600 RPM motor, it would need to be rated 80 HP or a 3.5:1 torque overload.

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