# Force, mass, & acceleration (sanity check)



## coulombKid (Jan 10, 2009)

vehicle mass: 1,500 kg
motor torque: 140 nm
low gear: 1.86:1
ring gear: 3.66:1
wheel radius: 0.33 meter

Neglecting all losses I calculate a rear axle torque (in low) of 953 nm.
With a 0.33 meter wheel radius I calculate a reaction force of 2,888 newtons.

Newtons law indicates that this contraption (neglecting losses & assuming 100% tire adhesion) would be capable of accelerating at 1.92 meters per second per second.

Assuming that 1 g is about 9.81 m/s/s that would indicate a maximum acceleration of about 0.196 gees. I rarely do this type of calculation and usually not in the metric system. How would this hypothetical vehicle drive? lead sled? rocket? Am I even close?


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## Duncan (Dec 8, 2008)

Hi Kid

60Mph is about 30m/sec so 2m/s/s will give 0 - 60 in 15 seconds

Your "low gear" is 1.86 : 1 ? - sounds like quite a high low gear


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## Joey (Oct 12, 2007)

1.92 meters/s^2 = 6.93 km/hr/sec

Under constant acceleration you could reach 95 km/hr (0-60 MPH) in 14 seconds. However without changing gears you would be at 5280 RPM. I know my motor will not have constant torque out past 2500 RPM.


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## coulombKid (Jan 10, 2009)

Joey said:


> 1.92 meters/s^2 = 6.93 km/hr/sec
> 
> Under constant acceleration you could reach 95 km/hr (0-60 MPH) in 14 seconds. However without changing gears you would be at 5280 RPM. I know my motor will not have constant torque out past 2500 RPM.


 If I used a Powerglide the torque converter, if used, would help. The maximum rpm recommended for the Kostov 13 is 4450 RPM. That would indicate that the governor should be adjusted to shift at about 50 MPH. Neglecting converter slip that would put the car at 94 MPH in high when the motor is at it's maximum recommended speed. The 140 nm figure came from their print. I've never seen a Kostov 13 used by any of our members so it's all bench racing at this point. I've got all the drag race parts for the TH700R4. Sounds like it would be a much better tranny choice once I weed out the mechanical fuse parts we're familiar with for the more modern automatic.


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## nulluser (Mar 4, 2012)

I will do it in English units for reference.

Weight = 3307 lbs
Mass = 102.7 slugs
Torque = 103.3 ft-lbs
Tire Radius = 1.083 ft
Final Ratio = 6.8076:1

Force = Torque / Radius * Final Ratio
Force = 103.3 ft-lbs / 1.083 ft * 6.8076
Force = 649 lbs

Force = Mass * Acceleration
Acceleration = Force / Mass
Acceleration = 649 lbs / 102.7 Slugs
Acceleration = 6.32 ft/sec^2
Acceleration = 0.196 g

Velocity = Acceleration * time
Time = Velocity / Acceleration 
Time = 88 ft-sec / 6.32
Time = 13.9 Seconds


This is all assuming constant torque of course.


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## MalcolmB (Jun 10, 2008)

nulluser said:


> I will do it in English units for reference.


Not wanting to be pedantic, but we switched to the metric system decades ago. I thought slugs were those slimy creatures that eat my lettuce 

Maybe you meant the Imperial system?

On topic: 0.2 g sounds a little undergeared to me. I've been aiming for 0.3 g minimum to cover odd situations such as steep hill starts and climbing ramps.


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## Woodsmith (Jun 5, 2008)

I think we call it imperial, the Americans call it English, because we started it.

Metric is much easier to work with given SI units, which I think maybe French.
Imperial is much more real world, at least for us older Brits.


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## bliksem (Aug 3, 2009)

It is called the imperial system because it is a royal pain in the butt to use.


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## Salty9 (Jul 13, 2009)

bliksem said:


> It is called the imperial system because it is a royal pain in the butt to use.


Too true and the reason I switched from an engineering major.


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## Ryan800 (Apr 15, 2010)

My car puts somewhere around 810 Nm to the wheels and weighs about 1125kg (with one person). My tires have about a .31m raduis, so this comes out to a theoretical low speed acceleration of 2.3 m/s2.

My car is very slow, and i'm going to put a larger motor in soon. However, it does start and drive up all of the hills in the area, of which there are many. It definitely does not go 0-60 in 15s because torque starts falling off around 25mph.

If you can get more torque or lower gearing, definitely do it. If not and you live in a flat area you are probably fine as long as you can accept very minimal performance. If you have hills, you will probably get tired of the slow starts pretty quickly, I know I did.


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## DIYguy (Sep 18, 2008)

Hey Kid.....

I would suggest that if you want to do a sanity check, you should ditch the math . . . 

I know that sounds a bit counter productive. . . but you are talking about putting a 13" diameter series wound motor in a 1500kg vehicle and you are worried about the torque. 

The problem here is that you are using the one hour rating for your max values. This value of 140nm is attained with a current of 300 amps or something like that. So, unless u are using a golf cart controller with tired floodies, I don't think u will have an issue. If you do, it's not because of the motor. 

That motor will easily take 3 times that one hour rating . . events that can be used for acceleration and climbing hills.  
With that motor and decent bit of energy feeding it, u could loose the transmission all together I expect.

Good luck.


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## coulombKid (Jan 10, 2009)

DIYguy said:


> Hey Kid.....
> 
> I would suggest that if you want to do a sanity check, you should ditch the math . . .
> 
> ...


After sleeping on it I realized I'd done a worst case based on S/60 specs. No one accelerates continuously. The print says the "peak" horsepower for this twister is 270. With a stout pack and a Solitron1 one would need to dump juice at a 250 volt by 1000 amp rate to realize the 270 hp peak (80% eff assumed). In Kostov's faqs they caution against exceeding the volt rating due to ones reliance on an RPM sensor and a shut-down routine in the controller. Without that, a drive line failure would turn the commutator into a really ugly flower. If the converter stall speed was mid band for the motor RPM, yes, the tires would slip OR the tranny would shell. Without a converter torque multiplication factor for the setup and a coefficient of friction for the meats it would be impossible to estimate acceleration. Once I crank the numbers for this hypothetical setup it is easy to see why Shiva the destroyer so easily turned that Porsha transmission into a can of loose gear teeth.


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## piotrsko (Dec 9, 2007)

the tranny and clutch on rebirths porsche was suspect in the first place. Shiva didn't do it any good, and seb helped a lot too.


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