5th gear calculation

[mark10337]

So I was looking at some calculations regarding a 5th gear etc.

Using the following givens:
Differential 3.54:1
Tyre 85.1 inch circumference

I make the following calculation


Gear_Gear____Gear*_Distance____speed per
____ Ratio____Diff___travelled____1000 RPM
___________________inches
1___2.95___10.44____ 8.15______ 8 mph
2___1.94____6.86___12.39______12 mph
3___1.34____4.74___17.94______17 mph
4___1.00____3.54___24.04______23 mph
5___0.63____2.23___38.16______36 mph


Which would allow travelling at 70 mph in 5th gear with 1944 RPM or in 4th gear at 3043 RPM. A 64% difference. Don't think that would equate to a 64% difference in fuel though :(

Fuel is about ?5.00 per gallon (?1.10 per litre * 4.54)
With an improvement of 4 mpg with the 5 speed it would also take about 100,000 miles to recover ?3,500 for the gearbox etc.

Another interesting calculation is the torque ratio.
Given the engine produces max HP at 5,400 RPM (Mine is the 4.2 litre with twin carbs) and max torque is at 4,000 RPM. The gears should ideally stay within this power band.

• ________Gear
  Max HP__Ratio___Reduction__Revs
  5400____2.95
  5400____1.94____0.66_____3551
  5400____1.34____0.69_____3730
  5400____1.00____0.75_____4030
  5400____0.63____0.63_____3402

Which shows the 0.63 is outside the optimal power band for the engine. A fifth gear with .80 would give a change in Revs to 4320, keeping inside the optimum power band. Although, is it necessary to stay in the optimum power band in 5th gear as may no longer be accelerating hard.

So it seems the .63 ratio would be the better way to go for leisure. Any error in logic or maths I will apologise for now :D

[Heuer]

Try redoing the calculations using this calculator: http://wahiduddin.net/calc/calc_speed_rpm.htm

My car with a 2.88 diff, 185 tyres and .8 5th gear allows me to cruise at 100mph at 3,000 rpm.

[mark10337]

seems the calculations are pretty close. If you had a .63 you would be cruising at 133 mph - although not quite sure that would be classed as cruising in the e-type.

Critically though, it keeps you in the optimum power band, although with the .63 you could have done the same speed for 700 revs less.

[Heuer]

That would depend on the diff ratio - 2.88, 2.98, 3.07, 3.31 or 3.54. The determination is the diff ratio not the gearbox.

[PeterCrespin]

quote="mark10337"]. Any error in logic or maths I will apologise for now :D[/quote]

Not that it matters a great deal but did you calculate your circumference based on rolling radius or just tyre dimensions? The latter would give you artificially high speed per 1000 rpm.

The optimum power band thing is slightly moot too, depending how you define it. There is a benefit from taller gearing that has to do with reduced cruise vacuum/pumping losses, due to the throttle needing to be open wider to produce the same power at lower revs. Depends what type of fuelling you use as to whether you gain mpg, but they are all fun factors to consider.

[mark10337]

Thanks Peter

Circumference was calculated from tyre dimensions - I might just get a tape measure out to get more accuracy :D

I did think the speeds looked somewhat on the optimistic side, but not far out. I put this down to being purely simplistic mathematical calculations without taking into account mechanical elements, friction, heat etc etc.

[Heuer]

The optimum power band for an E-Type is between 2,000 and 4,000 rpm because, on the road, torque is King. You will also get a more accurate figure if you use tyre radius - easier to measure, less error. We have been using the Shelguist Engineering calculator for several years so best to stick to the common standard if you want comparative results with others.

[markc555]

Assuming a healthy but otherwise standard engine I like the 0.73 5th gear with 3.54 diff combination. On standard 185 tyres (80 profile) it provides 30mph/1000revs for nice relaxed cruising and puts dual carriageway/motorway speeds (60-120mph, where legal of course) in the meat of the power/torque band.

This is the way I'll be going when I get round to fitting a 5spd 'box.

Cheers

Mark

[PeterCrespin]

You will also get a more accurate figure if you use tyre radius - easier to measure, less error.

If he uses the wheel radius measured at 9, 12 or 3 o'clock, or any other point besides vertically down to the ground, it will give the same results as the book value tyre dimensions he has already used.

I realise you know this David, but some readers may not realise the radius must be measured vertically down from the wheel centre, under normal load and pressure, to get the smaller 'rolling radius' that accurately informs the distance travelled per turn calaculation. It is always less than the circumference of the tyre.

Pete

[Heuer]

Indeed Pete, it was what I meant and should have spelled out.

Mark - have you considered changing the diff ratio to 3.07 rather than looking for a higher ratio 5th?

[mark10337]

Even better. Thank you Pete for the precision.

[markc555]

Mark - have you considered changing the diff ratio to 3.07 rather than looking for a higher ratio 5th?

Indeed I have. I've read most of the excellent information and well considered debate on the subject and feel that a 5 speed is the way to go for me. I find my existing set-up (US spec car with Stanglebergs and 3.54 diff) works really well around town and on country roads but is under-geared when you hit the motorway/freeway/autoroute/autostrada/autobahn.

While raising the diff ratio solves the high speed cruising issue it effects all the lower gears as well. Swapping a 3.54 diff for a 3.07 one is a about a 14% change. 14% lower revs on the motorway is good BUT 14% higher intermediate gears and associated slower response isn't so good. A case of not being able to have your cake and eat it. You could partially solve this by modifying the engine to make more power but I plan on keeping the engine standard.

A 5spd 'box with 0.73 5th and 3.54 diff gives and overall 2.58:1 mechanical ratio (before wheel and tyre circumference) and 30mph/1000revs on standard 185x15's. Meaning I can have my cake AND eat it 8)

Cheers

Mark

[christopher storey]

Mark : I suggest you have a drive in a car with 3.07 and, preferably, the EJ all synchro box which has higher intermediate ratios that the later KJ or KE boxes. Your 2nd gear probably produces a maximum of about 50 mph which is nearly useless for overtaking . The close ratio boxes enable 2nd to be used easily to 70 mph and at a pinch to 75, and make it a wonderful overtaking ratio . The 3.54 was fitted only to US cars where at the time virtually all states had a 55 mph limit, and it enabled the E to compete with the Corvette in the 0-60 drag so beloved of Americans. Otherwise, it has little to recommend it

[markc555]

Hi Christopher, I'm not a fan of "close ratio" 'box's in road cars. Admittedly my experience is in lower powered, and less torque'y, cars though. They're OK while the roads are flat but 2nd tends to be too tall for when it gets hilly or worse twisty and hilly so you end up screaming the engine in 1st gear on the steeper bits. I think they were developed before 5 speed box's were common for race/competition purposes.

The torque of the XK motor may well compensate for a tall 2nd gear in the hills/mountains but I still think 5 evenly spread ratios are the best answer for general road and touring use.

Cheers

Mark

[malcolm]

I'm not an expert, but I must say I can't agree with some of the comments aboput "high" 2nd gears.
My car has the 3.07 diff on a standard 4 speed box. Motorway cruising is thus relaxed with 70mph at 2800 revs - not high for an E. 2nd gear is great for overtaking/accelerating, with 60mph coming up at 4,600rpm, so well before the red line and not "screaming", but I would never have to go down to first on twisty or steep hills. The torque is such that it's just not necessary. I say that having driven through some tight, twisty and steep roads in France, and over the TT circuit on the Isle of Man. I'm shortly off to the Pyrenhees for 17 days, and have no concerns.
I'm not saying that a 5 speed box is wrong, just that there's not a lot wrong with the standard UK set up either.

[Heuer]

Most 5 speed boxes have similar ratios to the Jaguar box, fifth is simply an overdrive. I have a T5 and a 2.88 diff which is too high as it makes town driving a pain (first too low, second too high) and you need to slip the clutch in first on uphill hairpins. The 3.07 is ideal.

[andrewh]

I have a 3.07 in my 3.8 and find it pretty much perfect except on the motorway where I just feel an overdrive 5th would be nice. It's a luxury I guess but a nice option