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Calculating power to pull higher gearing?


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A totally academic question here:

I'm trying to understand how you would calculate an ideal power/torque delivery for a given gear ratio.

The example I'm using is the Ashcroft high-ratio transfer box on a Series III land Rover. My father has this set-up behind a healthy 5MB 2.25 petrol, standard 4.7:1 diffs and 750 tyres and I've always felt was over-geared for a 2.25. Lovely in 4th on a log run, but leaving 1st too high for strong hill starts. We were discussing this the other day and I found that my ignorance quickly started to shine through.

I'm aware that if the engine produced more power (for example if he were to throw lots of money at one of the ACR packages), that the gearing would quickly start to make sense.

But how would you calculate, in theory, how much more power or torque would be needed to allow you to maintain a strong 1st but with an overdrive-geared 4th?

I assume there would be some maths involved about how much power or torque is available at a given RPM but despite playing with ratio calculators I can't seem to work it out.

This isn't a question looking for advice on tuning a 2.25, nor about an engine swap - its simply me being frustrated that I can't adequately explain the theory of something.

I suppose the ideal is for me to be able to confidently calculate something like, 'for a Standard SIII gearbox with the Ashcroft high-ratio gearset the optimal output of an engine to pull that gear set is (for example) 101bhp@4000rpm/135lbft@2300rpm'

There is an incredible amount of knowledge on this forum so though I would ask if there was a formula that can be used for this, or is it more a question of feel? I have played with a number of ratio calculators but I'm not sure what I should be aiming for.

Many thanks indeed.

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The HRTC is overgeared regardless of engine - even if you have the low torque of a big engine to avoid stalling in the raised 1st gear, then it'll be juddering, which is no good for the Series gear box - Tdis and V8s produce far more torque than the box was designed for, and while the box copes admirably if driven sympathetically, juddering and thumping will eventually kill it. Furthermore, you lose engine braking for descents, which is not so much of an issue on road using HRTC, but generally just an issue off road in low range, which is why HRTC is a much better option than 3.54 diffs in a Series. The best option by a long way os overdrive, as you can just select it when needed and go back to standard low gears for low speed or hills. But with a Tdi or V8, that still leaves a Series under geared, and 3.54 diffs will still handicap the vehicle.

That leaves a choice of changing the transmission for something better suited to the engine, or using an overdrive with something like 4.1 diffs, which will avoid fabrication and chassis/cab alterations but will still be expensive and have some small compromise for low ratio unless you also fit the SII Suffix B low range gears (simple enough swap for the experienced, and not staggeringly expensive).

I don't know of a calculator for ideal ratios, but I'd use the LR ratios and engine figures as a rough template. The Defender transmissions are very flexible, though, with much taller top ratios than Series, and significantly lower low first, so you get the best of both worlds.

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Snagger's post sums it up pretty well.
The only thing I would add in an effort to satisfy your curiosity is if you added another calculation for rim pull or tractive effort as opposed to just engine torque which would possibly make the scenario more obvious. This would allow you to play with tyre sizes too. half an hour on Excel would see you right.
As an addition, the ability (as I understand it) for modern Land Rovers to have been able to tow 3.5 tons compared to most Japanese 4x4's which were more powerful was the ability to pull that weight from a standing start on a 16% grade. The series land rovers were only 2 tons which is a huge difference. Gearing being the only difference in the case of very early coil sprung ones.

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Funny I've never felt my 3.54s were a handicap!!

My mates S1 V8 was IIRC the last road car to win the AWDC trials championship on oh 3,54s!

The only issue is that the gearing affects the handbrake ability.

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The gears are simply there to allow you to access the engines power band.

If you had a magical engine which produced 100hp continuously from 1rpm to 5000rpm, you could have 1 really tall gear and it would work fine (assuming you also had a magical drivetrain which could withstand the torque required to produce 100hp at 1rpm :P)

So all you need to do is look at the power curve for your respective gear/operating conditions to figure out how much power you need.

If, with stock gearing, your doing 3000rpm at 60mph and with your new gearing your doing 2500rpm at 60mph, then you need to have the same power available at 2500rpm as you previously had at 3000 for it to pull the same.

Simply pick a few operating points on the curve and you can easily graph your desired output power curve to drive the new gearing.

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