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#1
07-02-2012, 08:32 PM
 Tatsushige Senior Member Join Date: Mar 2011 Location: Kanazawa, Kanagawa, Japan Posts: 225
Maths Help Please

I am doing some studying and looking at the Formulas and have a question on best range and stop-and-go range for a 24 volt, 20mph top speed system.

Best range = kilowatt-hour x 29
Stop go range = kilowatt-hour x 19

for a .528 kw-hour scooter with 2 x 22 amp-hour batteries, the results are

0.528 x 29 = 15.31 miles
0.528 x 19 = 10.03 miles

now the question is where the hell did the 29 and 19 come from?? I have gone back over the notes and cannot see where the 29 and 19 came from.

I am bad at maths and trying to learn all the Formulas

The next one is estimating top speed

Cr W + Cd A V2 / 391

Cr is Rolling Resistance factor
W is the weight in lbs
Cd is the coefficient of drag
A is the frontal area is square feet
V is the velocity in mph

torque required at the rear wheel - Force required x Wheel Radius .. So I take it 391 is the torque required??

Units

Amps – measure of electric current flow
Volts – measure of electromotive force
Ohms – measure of resistance to electric current flow
Watts – measure of electric power
Amp-hours – electric current capacity (e.g., for a battery)
Watt-hour – electric energy (e.g., for battery pack)
Watt-hour/pounds – electric energy density (e.g., for different battery technologies)
W – weight in pounds
Cr – coefficient of rolling friction
Cd – coefficient of drag
A – area in square feet
V – velocity in miles per hour (mph)
f - angle of grade

Formulas

Volts = Amps x Ohms – Ohm’s Law
Watts = Volts x Amps – electric power
Watt-hours = Amp-hours x Volts
Kilowatt = 1000 watts
Horsepower (hp) = Kilowatts / .745
1 horsepower = 550ft-lb/sec
Wheel rpm = (mph x revolutions/mile)/60
Power (ft-lb/sec) = torque (ft-lb) x speed (radians/second) = force x velocity
Volts – resistance x Amps
Force = Wsinf + Cr WCosf + cd A V2/391
Torque = force x moment arm length (e.g., radius of the wheel)
Best range (Miles) = kilowatt-hours x 29 for less than 1000 watt-hour
Stop-and-go range (miles) = kilowatt-hours x 19 for less than 1000 watt-hour
Charging time (hours) ~= amp-hours / DC Amps
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Last edited by Tatsushige; 07-02-2012 at 10:31 PM.
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#2
07-03-2012, 02:19 AM
 PStechPaul Senior Member Join Date: May 2012 Location: Cockeysville, MD 21030 Posts: 1,183
Re: Maths Help Please

I think the 29 and 19 figures are just approximations based on users' experience. The figure I have seen for car type EVs is 330 W-Hr/mile. Since a scooter is roughly 1/10 the size and weight, I would expect the figure to be about 33 W-Hr/mile. So in that case your 528 W-Hr scooter would go about 16 miles. Pretty close to your calculations.

There are a lot of factors involved. I am going to do some data collection and analysis when I get my electric tractor running again. But it appeared that it was moving pretty well with 24 VDC and 20 amps, or 480 watts. My batteries are about 15 A-Hr (360 W-Hr) but you can only expect about half that, so I might be able to go for about 20 minutes. I was only going about 1 MPH but that was on rough ground and slight hills so I could probably go 3 MPH or about 1 mile. Probably 100 W-Hr/mile. I plan to install two 100 A-Hr batteries for 2400 W-Hr, so with that I can probably go 12 miles or so.

As they say, YMMV. The more measurements you can take, the better you will know what your scooter can do. And a real-time monitor may help you adjust driving style to achieve better range, or determine how much aggressive driving or hill climbing or other factors affect your performance.
#3
07-03-2012, 04:11 AM
 Tatsushige Senior Member Join Date: Mar 2011 Location: Kanazawa, Kanagawa, Japan Posts: 225
Re: Maths Help Please

I am looking at building another Cheetah bike, but this time with a new PMG 132 motor at 72 volts.

The PMG 132 RPM is 45/V ... So if I am correct the max rmp is 45 x 72v = 3240 rpm ... running a drive sprocket of 11 and a rear sproket of 72 should give a speed of about 45mph .. Correct?.

This time I plan on using the SciB , 72v =12v x 6 packs at a total weight of 6kgs

1 x 12 volt pack (5 x 2.4V cells) 4.0Ah Nominal Capacity, Maximum Discharge Current 8 A (Continuous) 25 A (≤ 0.3 Seconds)

So is the maths

4.0 Ah x 72V = .288 kw-hour
or
6 x 4.0Ah x 72V = 1.728 kw-hour

First bike I used the items in the build manual, but this time I am going a different road, so trying to learn how to work all the maths involved!
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#4
07-03-2012, 06:41 AM
 Coulomb Senior Member Join Date: Apr 2009 Location: Brisbane, Australia Posts: 716
Re: Maths Help Please

Quote:
 Originally Posted by Tatsushige The PMG 132 RPM is 45/V ... So if I am correct the max rmp is 45 x 72v = 3240 rpm
That's an unusual way of quoting the motor constant, but it sounds reasonable.

Quote:
 ... running a drive sprocket of 11 and a rear sproket of 72 should give a speed of about 45mph .. Correct?.
That depends on the effective diameter of the tire. You are gearing down by 72:11, so at top speed (neglecting controller overheads) the wheel will revolve at 11/72 x 3240 = 495 RPM = 495/60 RPS or 8.25 RPS. If a 26" tire is used (and assuming it has an effective diameter of 26" when loaded), that's 26 x 8.25 x 3.14 (using circumference = diameter x pi) = 674 inches per second, or 56.1 ft/sec or 202 000 ft/hr or 202 000 / 5280 = 38 MPH. (That really is easier in the metric system.) You'd need a very large wheel to make 45 MPH, if my maths is correct.

That assumes that the battery and motor can supply the power required to overcome rolling friction and drag at that speed.

Quote:
 1 x 12 volt pack (5 x 2.4V cells) 4.0Ah Nominal Capacity, Maximum Discharge Current 8 A (Continuous) 25 A (≤ 0.3 Seconds) So is the maths 4.0 Ah x 72V = .288 kw-hour or 6 x 4.0Ah x 72V = 1.728 kw-hour
So I'm assuming that this pack is 30s1p (30 cells in series, none paralleled). The 72 V is already taking into account the 30 cells (or the 6 packs of 5 cells), so you don't multiply by 6 again. When you put 30 2.4 Ah cells in series, you still have a 2.4 Ah pack (things in series have the same current) but 72 V (the voltages add).

So your first calculation is correct: 4.0 Ah x 72 V = 288 W = 0.288 kWh.

Last edited by Coulomb; 07-03-2012 at 06:51 AM. Reason: Forgot a [ /quote ]; added assumption about adequate battery and motor power
#5
07-03-2012, 07:03 AM
 Coulomb Senior Member Join Date: Apr 2009 Location: Brisbane, Australia Posts: 716
Re: Maths Help Please

Quote:
 Originally Posted by Tatsushige The next one is estimating top speed Cr W + Cd A V2 / 391 Cr is rolling resistance factor W is the weight in lbs Cd is the coefficient of drag A is the frontal area is square feet V is the velocity in mph torque required at the rear wheel - Force required x Wheel Radius .. So I take it 391 is the torque required??
No; this formula seems to give the force required, and as noted torque required is this force times the wheel radius. If the result was torque required, the wheel radius or diameter or circumference would have to be part of the formula.

I also assume that there are brackets missing, and that V2 should be the square of the velocity, sometimes written as V^2. I'd say the 391 is just a constant required to convert the horrible (sorry) units: there are pounds, square feet, and miles per hour squared, and the result has to be in units of force (I'm guessing pounds of force). So you figure out the force you get from the vehicle from the torque of the motor, adjusted for gear ratio and transmission losses, and when that balances the total force due to rolling friction and drag, the vehicle will stop accelerating, i.e. it will be at its top speed (on a level road).
#6
07-03-2012, 06:42 PM
 Tatsushige Senior Member Join Date: Mar 2011 Location: Kanazawa, Kanagawa, Japan Posts: 225
Re: Maths Help Please

Quote:
 Originally Posted by Coulomb No; this formula seems to give the force required, and as noted torque required is this force times the wheel radius. If the result was torque required, the wheel radius or diameter or circumference would have to be part of the formula. I also assume that there are brackets missing, and that V2 should be the square of the velocity, sometimes written as V^2. I'd say the 391 is just a constant required to convert the horrible (sorry) units: there are pounds, square feet, and miles per hour squared, and the result has to be in units of force (I'm guessing pounds of force). So you figure out the force you get from the vehicle from the torque of the motor, adjusted for gear ratio and transmission losses, and when that balances the total force due to rolling friction and drag, the vehicle will stop accelerating, i.e. it will be at its top speed (on a level road).
These Formulas are from a US build, I am an Aussie and trying to convert them in metric.

To up the Ah one needs to have the cells connected in parallel ??

I am trying to remember crap from the age of 15 to 18 when I was a motor rewinder in Perth, now over 40 the brain cells have been mostly killed off by booze.
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Gasoline?! That is so last century!
#7
07-03-2012, 06:54 PM
 PStechPaul Senior Member Join Date: May 2012 Location: Cockeysville, MD 21030 Posts: 1,183
Re: Maths Help Please

The most important spec for a battery pack is W-Hr, which is essentially the voltage times the current since it's DC. The usable W-Hr depends on how deeply you dare discharge the batteries and also on how well your controller handles lower voltage as the batteries discharge. A controller which provides a constant power to the motor will draw more current as the battery voltage drops, and a constant torque controller will draw constant current but as voltage drops the motor speed will drop and you lose power. If you try to regain speed you will draw more current and the motor will become less efficient. So things go to hell in a hurry at the "end of days" from a battery's perspective.

It's best to have enough batteries to get the highest voltage possible within the specs of the motor. And then you must consider the peak currents available from the battery pack when you use PWM to control the motor. A good size capacitor bank may help tremendously.
#8
07-03-2012, 07:14 PM
 Tatsushige Senior Member Join Date: Mar 2011 Location: Kanazawa, Kanagawa, Japan Posts: 225
Re: Maths Help Please

The last Cheetah I built was like the manual.

Etek Motor, 48V, drive 12, rear 72, peak rpm about 3500 giving a top of about 45mph.

At the time I wanted to use 72volts and the Scib batteries but could not get my hands on them, this time I can.

Just reading this morning Toshiba has a new Scib battery with 20ah rating. This may be a lot better for the new project as it would give 1.440 kw-hours and not .288 kw-hours

I am dropping the steel tubing this time and getting the R&D company helping with the car to make a CF frame, making the bike a lot lighter, and think I will drop the chain driven and go belt, as chain drive drove me nutz after 20 minutes.

Reading Thunderstruck site the PMG is best suited to the Alltrax controllers, from 24-72 volts or Sevcon Millipak.

Also looking at a E-Kart and was told that Thunderstruck got 110mph from a E-Kart with a AC-20 back in 2009. This would be a Xmas project.
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Gasoline?! That is so last century!
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