5 Speed Gearing question

[stuartgb100]

Can someone please give me the mph/per 1000rpm for the Lotus 5 speed box for the 3.9, 4.1 and 4.44 diffs, please ?

The manual gives 5 speed ratios as 3.2:1, 2.01:1, 1,37:1, 1.00:1 and 0.80:1.

Alternatively .......... the formula !!

Regards and thanks,
Stuart.

[msd1107]

Stuart,

The attached spreadsheet has a variety of sheets to answer various questions that most people do not ask.

Sheet RPMGear gives MPH/1000 RPM for a variety of gear ratios. You can input your tire size, and diff ratio.

The spreadsheet is ZIPped and renamed to .XLS so that LotusElan.net will accept it.

Download the file. Rename it to .ZIP. UnZIP it, then use in a spreadsheet program.

David
1968 36/7988

[Esprit2]

Stuart,

Since you inquired about MPH/1000 rpm, I'll presume you're interested in inches and feet... not metric measures.

The easy way is to start with a published value for MPH/1000 rpm (manual, magazine road test, etc), or to head for the freeway mile markers with a stop watch and measure your car's actual MPH/1000 rpm. Then simply apply gear ratio proportions to that value.

If you determine your car goes 17 mph/ 1000 rpm now with a 1:1 top gear in a 4-speed trans (I pulled that number out of the air), what will the value be with an overdrive 0.080:1 top gear in a 5-speed?

New mph/1000 rpm = (Old mph/1000 rpm) x (old ratio / new ratio)
New mph/1000 rpm = (17 mph/1000 rpm) x (1.00 / 0.80)
............................ = (17 x 1.25) mph/1000 rpm
............................ = 21.25 mph/1000 rpm in 5th gear

That works for comparing final drive ratio changes, or for comparing mph/1000 between gears in the transmission.


If the 21.25 mph/ 1000 rpm value for 5th gear occurred with the 3.9: final drive, what would it be with a 4.1:1 rear end?

New mph/1000 rpm = (Old mph/1000 rpm) x (old ratio / new ratio)
New mph/1000 rpm = (21.25 mph/1000 rpm) x (3.9 / 4.1)
............................ = (21.25 x 0.95) mph/1000 rpm
............................ = 20.21 mph/1000 rpm at 4.1:1 final drive


Or, using the ratios you posted and the (made up) 21.25 mph/1000 rpm value for 5th gear, what's the proportional value for 3rd gear?

New mph/1000 rpm = (Old mph/1000 rpm) x (old ratio / new ratio)
New mph/1000 rpm = (21.25 mph/1000 rpm) x (0.80 / 1.37)
............................ = (21.25 x 0.584) mph/1000 rpm
............................ = 12.41 mph/1000 rpm in 3rd gear.

Remember, I just pulled 17 MPH/ 1000 rpm out of the air as an example. Don't take it as real.

*~*~*~*~*


If you insist on calculating a MPH/1000 rpm value from scratch, then the real world value will depend upon the size tire used, the inflation pressure and the load. A larger tire rolls further forward in one revolution than a smaller tire. An over inflated tire will roll further than an under inflated tire.

Given an effective rolling radius, in one revolution a tire will roll forward a distance equivalent to it's circumference, or 2(Pi)r.

MPH at 1000 rpm = (1000 rev/min) x 2(Pi)r inch/rev
........................ = 2000(Pi)r inch/ minute
12" = 1 ft
5280 ft = 1 mile
60 minutes = one hour
Pi = 3.141592654

So, calculating and converting units...
MPH at 1000 rpm = 5.949986086 x r MPH, or...
MPH = 5.949986086 x r MPH/1000 TIRE rpm

Engine RPM = Tire RPM x (trans ratio x diff ratio), so...
MPH = (5.949986086 x r) x (trans ratio x diff ratio) MPH/1000 rpm.

But you still don't have a good value for r. You could ignore the effects of tire inflation and load upon the tire's rolling radius and just use the tire's geometric radius calculated from it's size. Or, you could measure your car's tire's rolling radius directly and ignore how it squirms as it rolls under deflection at spead and drive load. Or, once again going back to gathering emperical data, you could directly measure how far the tire moves forward in one tire revolution... ignoring speed effects.

Put a mark on the tire at the center of the ground contact patch. Roll the car forward a few tire revolutions, stopping when the mark is again at the center of the contact patch. Measure how far it traveled and divide by the number of tire revolutions to get it's circumference, 2(Pi)r in inches.

Divide that number by 2(Pi), or 6.283185307... to get the effective radius, r. Use that in the formula above to calculate the MPH/1000 rpm... ignoring tire "slip" under drive load.

Once you have the MPH/1000 rpm value, go back to the top and use the proportional method to bounce between different gear ratios.

As you can see, there are a variety of variables that affect a calculated value. If you're a math student looking for a challenge, knock yourself out. Otherwise, the best way to get to a workable MPH/1000 rpm value is to go to the freeway and measure it at the road speed in which you are interested. That will be a real world number accurate to your measuring capability, and better than any approximated values.

The magazine road test and Workshop Manual values (when available) are measured road values. Save yourself some headaches and do what they do... measure a baseline value.

Regards,
Tim Engel

[stuartgb100]

Thanks for the spreadsheet and formulae.
Much appreciated.

Regards,
Stuart.