Brammo Empulse R gear ratio and torque

[frodus]

I wanted to post some gear ratio and torque/force I calculated for the Brammo Empulse R.

 

Motor Peak Torque: 90N-m (66.38ft-lbs)

Rear tire: 180-55 ZR17 0.32m (1.033ft) radius

Transmission Gear Ratios:

Primary: 35T/59T = 1.69:1

1st: 14T/30T = 2.14:1

2nd:16T/28T = 1.75:1

3rd: 20T/29T = 1.45:1

4th: 22T/27T = 1.23:1

5th: 24T/25T = 1.04:1

6th: 20T/19T = 0.95:1

Final Drive: 14/38 = 2.71:1

 

Torque at rear axle:

1st: 882.09 N-m or 650.60 ft-lbs

2nd:721.33 N-m or 532.03 ft-lbs

3rd: 597.68 N-m or 440.83 ft-lbs

4th: 507.00 N-m or 373.94 ft-lbs

5th: 428.68 N-m or 316.18 ft-lbs

6th: 391.58 N-m or 288.81 ft-lbs

 

As a fun little exercise, I wondered how much force is that on the road from the rear tire? I did this wrong the first time by using ftlbs and newton-meters interchangably, thanks to Protomech for questioning me, I was rushing

 

We know Torque = radius * force * sin(90). We have torque, so the equation becomes Force = torque* 1/r

The angle is 90 degrees since the road is tangential to the tire, so its just 1. So one newton-meter of rotational force would equal one newton of force at 1 meter away. My "rear tire ratio" is 1/r, or 3.13. If calculating using feet, the ratio is 0.97.

 

Rear Tire ratio: meters: 3.13:1 (feet 0.97:1)

 

Rear tire peak force at rubber:

1st:  2760 N or 620.47 lbf

2nd: 2258 N or 507.62 lbf

3rd: 1871 N or 420.62 lbf

4th: 1587 N or 356.77 lbf

5th: 1342 N or 301.69 lbf

6th: 1226 N or 275.62 lbf

 

 

Here's some tools to convert from N-m to ft-lbs and from Newtons to lbf (pound force):

http://www.unitconversion.org/energy/newton-meters-to-foot-pounds-conversion.html

and

http://www.unitconversion.org/force/newtons-to-pound-forces-conversion.html

[Jeff]

Thanks for putting that together.  I've been wondering about this, actually.  The official specs state 880 Nm . . . wonder what the discrepancy is.

Also haha what happens when you are an idiot like me and go up 4 rear teeth?

In either case, the answer is 'a lot.'

[frodus]

Not sure about the discrepancy.... I got the gear ratio from Brammo directly. I calculated the rear tire moment.... As about 0.97.....not sure if maybe the peak torque is a little higher for locked rotor... AKA a complete stop.

Will defer to Brian.... Lol

[protomech]

Brammo's specs lists a 48 tooth rear sprocket. But 38 tooth rear appears to be correct, as Jeff and BrammoBrian both mention moving to a 42 tooth rear for increased acceleration.

Brian mentioned a little while ago that the Empulse is available in the Gearing Commander database. The site lists 1st gear at 30/14. The other gear ratios match what you have.

30/14 for 1st gear matches FreepZ's reports of 38 mph at 5000 RPM 1st gear, 47 mph at 5000 RPM 2nd gear. 38 mph * (30/14) * (16/28) = 46.5 mph. That would put 1st gear torque at 506 Nm matching the rest of your calculations.

How are you using the rear tire ratio term?

I don't understand where the 880 Nm figure comes from either.

The Empulse R has roughly 90Nm of peak torque to 4500rpm.  Running that through the gearbox and final drive equates to well over 800Nm at the rear wheel in first gear and over 700Nm at the rear wheel in second gear.

Maybe we're missing another term, or the front sprocket is smaller than indicated, etc. The calculations for 2nd gear torque are also well under 700 Nm.

At 38 mph, the 12.4" radius wheel is turning 515 RPM. FreepZ states the motor in 1st gear indicates 5000 RPM at this speed, so the overall gearing ratio should be approximately 9.71.

90 Nm of motor torque x 9.71 gearing = 874 Nm at the rear wheel.

So I think Brammo's torque claims are accurate given the measured RPM data, but we're missing something else. Maybe there's another set of reduction gears?

[frodus]

I'm thinking first gear is botched. It's the same as what I have for final drive... Will ask tomorrow. It's a start. Just good info to have.

[BrammoBrian]

You're missing the primary ratio between the motor and gearbox, which is 1.70.  This should be multiplied across all the individual gearing ratios and through the final drive.  You'll see well over 800 Nm in first gear at the rear wheel.

[protomech]

Okay. There we go. Leaving aside the tire ratio term for now.

1st: 890 Nm (= 90 Nm * 1.7 primary * 30/14 1st gear * 38/14 front/rear sprocket)
2nd: 727 Nm
3rd: 602 Nm
4th: 510 Nm
5th: 433 Nm
6th: 395 Nm

[Shinysideup]

Ok then. All we need now is a second column for Jeff, Brian, and me that have thrown on a 42T rear sprocket.

In this case, I believe the Final Drive: 14/38 = 2.71:1 becomes 3:1.

And we should have everything translated into foot-lbs. for the Harley folks reading this.

Maybe we need (hint) a spreadsheet posted. I'm not a math whiz, but, intuitively, I'd sum things up as: "Hauls butt."

I was parking the other day when I saw a young dude pull up to turn into his driveway in a Mercedes twin turbo V12. After complimenting him on his ride, I grinned and said, "You know, with my 54 hp, I can blow you away for half a block!" Wisely, he didn't take the bait.

[frodus]

I'll see if I can come up with a little spreadsheet tomorrow sometime.

Thanks Brian!

[frodus]

Edited my entry. I had the rear tire ration in feet but I was working in Newton meters. Thanks protomech for keeping me honest. Corrected and added some links. Also corrected the Ratios. I got two sets of ratios and the second one was correct and included the primary ratio. Should be ok now.

Also added lbf and ft-lbs calculations.

[flar]

I decided to make my own google spreadsheet for the calculations above.  The results are slightly different so perhaps I got some of the math wrong?

In any case, I'm sharing it as "view only", but if you have a google docs account you can save a copy and edit your own copy.  Let me know if you spot a mistake and I can update the original:

https://docs.google.com/spreadsheets/d/1_avF3jxl3s0lEa3FB7WdIIKnREKzhvZdi2jMMvzpF1M/edit?usp=sharing