Differential (Diff) ratios

Competition engines and ancillaries - general discussion
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miro-1980
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Differential (Diff) ratios

Post by miro-1980 » February 18th, 2009, 2:22 am

Guy,

I will be changing to Abarth differential with 7/43 ( highest ratio ever used as far as I know ) CORRECTION: THE HIGHEST WAS : 6:41 ( OR 6,83 !!!).

I have calculated speed on basis of standard differantial ratio (12/43) - currently installed and the one I am planning to install (original abarth differential with 7/43 teth ratio).

I have used the Diffsonline calculator to make the calculation and the results look strange. Are they OK?

Note : I have recalculated the the data is to show km/h (not mph by) multiplaying the mph results by 1.609.

These results look strange. What worries me is 209 km/h at 6000 RPM on standard gearbox and standard diff ratio of 12/43.

Do they look OK to you ?

I am attaching both the result sheet in pdf as well as the as well as the calculator with the same calculation. Please verify if you can ?

M
Attachments
diffsonline.xls.pdf
(46.4 KiB) Downloaded 362 times
diffsonline.xls
(500.5 KiB) Downloaded 312 times
Last edited by miro-1980 on February 24th, 2009, 3:22 pm, edited 2 times in total.
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Guy Croft
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Re: Differential ratios: Is this right ?

Post by Guy Croft » February 18th, 2009, 2:55 pm

Looks OK to me Miro. I checked out the presets of diff and tyres and got the same results.

209Kkm/hr on 12/43 diff at 6000 rpm - in other words about 130 mph. What can I say?! To get to 130mph on a 2 liter 8v Fiat at 6000rpm it would have to be quite well supercharged....

G

miro-1980
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Re: Differential ratios: Is this right ?

Post by miro-1980 » February 18th, 2009, 4:48 pm

Guy, that is exactly my thought !

By my experience the car I drive could (theoretically reach 210 km/h at 8000) by simple calculation based on the speedometer and tachometer changes while driving - assuming that these factors change linearly - which of course they are not due to such factors as air one drives through.

I would have and additional question, though:

If I put 7/43(or 6.14) diff, what will be the actual driving effect? What do I gain / lose. I was told the car will get onto high RPM more quickly, forcing me to shift up much quicker than previously, the car will have better acceleration and more "power on wheels from start" as well as quicker pickup on short stretches (especially up hill). It will lose significantly on top speed (is the calculator showing true speed loss proportion of 40%?)

Our track day courses are fairly short ( 2-3 km a run) and designed such a way as not too gain to much speed ( shikanes, sharp turns, partially going on go-cart track or the course - not the big oval ring, etc.) This seems to favor cars with very good acceleration (not so much power as torque). To what extent o makes sense in such case to go with very high diff ratios. Currently I have a choice of 7/43/, 8/43/adn 10/43.

I race on a normal racetrack ( 3 x 4.5km course) only once a year and this is mainly for fun- not points. There is one rally in pour classification : mainly uphill starches with a lot of sharp curves , each stage has ca. 3 km in length.

Any ideas? Suggestions?

Attched three examples :
planimprezy.pdf
track day 1
(129.04 KiB) Downloaded 285 times
ulez.pdf.pdf
track day 2
(229.68 KiB) Downloaded 242 times
Attachments
PS_1_2.jpg
track day 3
PS_1_2.jpg (85.88 KiB) Viewed 6376 times
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Re: Differential ratios: Is this right ?

Post by Guy Croft » February 18th, 2009, 5:31 pm

Miro, hi

good questions and it gives me a chance to explain how to work these things out.

If I got my maths right that diff is way too low for circuit, 7/43 (reduction of axle speed by ratio of -6.3) well, that's a forest rally diff. That's a low diff - remember a small pinion is driving a large crownwheel and 43 turns of the pinion give 7 at the wheel - not the other way round. 10/43 would be a taller choice. 43 in, 10 out. It might accelerate quicker than a taller diff but the straight line speed on your circuit will need to be 120mph or more.

The graph below is reproduced from the Excel data download and you can enter the key variables of diff and gears. The graph shows how a gearbox generates road speed in each gear and shows that if you change up at say, 7200 rpm you will get a certain rev drop as you engage the next higher gear. Your gearset has huge rpm drops and changing the diff will not later that, merely increase the attainable speed in each gear. In fact the only truly 'close' ratio in the whole gearbox is 5th!

A race close ratio gearset will ideally only give about 1000 rpm drop which means you can (allowing for the time lag of 0.5 - 1 sec or so for the gearchange) keep the engine to the right side of peak torque (for best power) in every change. Of course, the more gears you have the less tall 1st gear needs to be to achieve a high straight line speed. A very tall first gear with a peaky engine means a hard load off the line on the clutch because you have to 'slip' it to get going. This is how gearsets and powerbands are assessed professionally in the early stages of engine design. For my own part - if the gearset, diff and engine don't comfortably get you to 65-70mph in second gear, that is just not going to be a happy combo to drive.

If you use a taller diff (in other words one that gives less reduction of axle speed for given engine rpm) you'll get a higher straight line speed but on the downside, the engine will naturally need 'more power' to sustain that because of the increase in drag. I say that in 'inverted commas' because the engine might well have enough, but if the diff is too low, you'll never be able to put it to use.

I'd be for using something like a 10/43 diff and get hold of a Type ( Ford 5 speed gearbox (I have an adaptor for that to the 131 5sp bellhousing) and a TranX gearset. See:

http://www.tran-x.com/gearkits/f5spt9.html

They are a super firm and can build a complete donor box. I would trade 40bhp for a TranX gearset any day.

They have numerous ratios available, you can see how tall their 1st gears all are, you can enter them and you'll be able to make your own graphs and optimise your chances of getting a decent race.

I hope this gives you some pointers.

GC
Attachments
Miro diff 7_43.GIF
Miro diff 7_43.GIF (17.56 KiB) Viewed 6363 times
Engine Road Speed Calculations 7_43 diff Miro.xls
road speed by gear calculator and many thanks to GCRE client and forum member Melvin Floyd who took the time to write it and let me 'borrow' it.
(27 KiB) Downloaded 284 times
Miro diff 10_43.GIF
your car with a 10/43 diff - note the increase in top-end speed.
Miro diff 10_43.GIF (14.73 KiB) Viewed 6363 times

miro-1980
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Re: Differential ratios: Is this right ?

Post by miro-1980 » February 19th, 2009, 2:58 am

Guy, it took me a while to chew on it !

Very interesting !

I have never driven a car with such a low diff ratio, and your data ws most helphul.

I am happy to have a choice of 7/43/, 8/43/ and 10/43 diff ratios which will help.

It looks like 10/43 will be the best for the circuit, though the 1/73 may be good for a hill climbing.

Thanks again

Miro

PS : It looks like a close rato gearbox is a must!

M
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mickwood
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Re: Differential ratios: Is this right ? CORRECTED

Post by mickwood » March 2nd, 2009, 7:47 pm

Guy/Miro

A bit late in the day, but I would like to add a bit to this.

Firstly i dont quite espouse the notion that you should optimise gearchange points so you change up at peak power. I think you need to go past this as you will optimise the acceleration if you change up at the point where the engine power has decayed to the point on the power curve, where it equals the power you will achieve in the new gear.

Think of an engine producing say xbhp at 6000 rpm, and the same xbhp at 7,200rpm (one going up the curve, one coming back down), but peaking (at say1.05x) at (say) 7000 rpm. Assume the gear ratio interval is a multiple of 1.2. With this set up the optimum gearshift point would be at 7,200 rather than 7000 (Note - i have picked these numbers simply to make the mental maths easy)

I did have a little excel programme that demonstrated this, but sadly it is an old laptop that i cannot access. That program allowed you to input the torque characteristics of a given engine, the gearbox ratios, Axle ratio and wheel size and it would plot the overlapping power curves in each gear with the y axis as roadspeed. if you think how the output of that would look, you can visualise the logic as it maximises the area under the curve. This also allowed you to optimise gearchange points in each gear. It also plotted torque at rear wheels by roadspeed (5 curves, one for each gear) and that demonstrated the same thing.

Of course, hanging onto the lower gear puts more stress on the engine, but that where Guy comes in!

As Guy has pointed out, ideally, you should narrow the rev drop to keep the engine as close to peak power as practical, which means fitting CR gearsets. Of course, most of us are limited to 5 speed boxes so you cannot make the ratios too close, as you will have too narrow an effective speed range. Normally, even on CR gear sets you will find the gap from first to second is much wider to help overcome this. The corollary is that you have to hold on to first for longer than the other gears.

The other thing that programme helped disprove was the notion that "a lower diff gives faster acceleration"
Yes its true that a lower diff will get you off the line quicker, but it makes practically no difference once you have got off the line. It also means you lose on top speed. So unless you have a lot of first gear corners such as hairpins, it better to go a mite longer than you might think.

Before i hear some of you screaming that i am not right, think about the same engine listed above> Assume you have a gearbox where the ratios are all a 1.2x multiple of each other. Assume you have a choice of diffs, a 4.0 or a 4.8 Ratio. Effective ratio at the wheels is affected by both Gearbox and back axle. (its also affected by wheel size, but lets assume that is a constant for now)

Dropping in the 4.8 diif in this theoretical set up, effectively gives the gear set another whole gear lower than first with the high ratio axle, but sacrifices the old top gear to achieve this
However performance in the old first second third and fourth will be identical to the new second third fourth and fifth.
Of course the car "feels" more responsive with the lower ratio (as you are having to swap cogs quicker) but it is only an illusion.

As a basic rule of thumb the old rule holds good - try to gear the car to the top speed you want to achieve, and then adjust the gear ratios to match your use up to that.

On the 131, i found that the low ratio axle (7/43 or 6.14x) was essential use with the overdrive close ratio CIMA box, if i was running TB15s on the 15" rims, That combination produced a max top speed of around 107mph (170kph) at 7200, which was fine for the sort of demo work we were doing. If i fitted the DD top box, then i needed to go longer on the ratios, and used a 4.875x normally, or even a 4.3X if i was running Avon slicks (with their much lower rolling radius).

The most oddball set up i ever ran was the ex Ivory Coast Rally winning Group B Toyota Celica twin Cam turbo. I was lucky enough to drive it with Waldegard in a demo in Germany. That car was exactly as it had finished the rally and was geared to over 140mph flat in top and still in tall forest tyres although we were running on Tarmac. The car was almost impossible to get off the line on tarmac (especially on one start which was slightly uphill). However the tall gearing did mean that we were still accelerating hard at the end of a 500 metre flat straight, and the forest tyres made the following square left "interesting". (by contrast, the 037 was flat in top after about 100 metres of this)

miro-1980
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Re: Differential ratios: Is this right ? CORRECTED

Post by miro-1980 » March 2nd, 2009, 10:44 pm

Mickwood,

What you wrote was the kind of comments I looked for.

Despite asking some pretty advanced competition question I am really a"rally rookie", having never driven a real competition rally car.

For the last couple of years I have been playing with my 131 on a circuit of ClassicAuto Cup which consists of the three tack days and a one real rally. I as I said so far I was doing it with ca 130bhp engine at 5500 with 180Nm torque at 3500). Majority of cars participating are really "tuned up standards" but the top 3-4 are really well sports prepared. I got slightly uncomfortable (to put it gently ) ending in 4th or 5th position all the time. So I decided to go out and get the car prepared for such events. My top 3 contenders are Alfa GTV
(190 hp the best prepared classic car in Poland well beyond my reach), Ritmo Abarth, and Ford Escort RS ( both ca 160 hp and within my reach)and Mazda RX 7 (also well within my reach).

The car I drive has stiff adjustable suspension, a 12/43 diff and stands on 205/60/13 Toyo road slicks.
12-43 diff standard gearbox.JPG
12-43 diff standard gearbox.JPG (103.01 KiB) Viewed 6040 times
My problem was that the track days are designed in such a way as to limit the top speed (for safety). The straights are pretty short (200 meters long tops). I would typically drive all track on 2nd and 3dr gear. The curves are tight and I would often reduce into 1st. Most straights are 100m. Handling of the car is very much a key factor ( I have this under control) The problem is acceleration especially at gear change. I noticed than when I was leaving a curve on 2nd with 6000 rpm and shifting into 3rd (full throttle) it takes some time before the car responds with good acceleration. This would be especially viable between 2dn and 3rd. This is when I was missing acceleration.

Now I am building hopefully a 180 hp engine ( on "forged everything and 275 degrees competition camshafts ) which should give me te power egde I want. I am also planning to install the original 131 abarth diff . The probem is - as it turned out -9 ( see viewtopic.php?f=6&t=1794) I have only two ratios available ( 7/43 and 10/43). I do not not which to install.

Secondly I started to look at the gearbox issue I realized that all of this is very much interconnected (gearbox/dff/power/torque/rims/tires). and that no combination has really a universal application. I do not want to change the diff ratio from event to event. I certainly also wold rather drive the car to the event (rather than have it hauled.)

So what I facing is a series of decisions:

1/ which diff ratio to install
2/should I change into CR gearbox

I am currently inclined to the as follows:

Install 10/43 and keep the current gearbox.
10-43 diff standard gearbox.JPG
10-43 diff standard gearbox.JPG (109.54 KiB) Viewed 6037 times
Or go for 7/43 and install a CR gearbox.
7-43 diff CR gearbox.JPG
7-43 diff CR gearbox.JPG (107.12 KiB) Viewed 6039 times
Or should I forget half means and go for 10/43 on a CR gearbox?
10-43 diff CR gearbox.JPG
10-43 diff CR gearbox.JPG (102.41 KiB) Viewed 6033 times
Could give me some comments on this..

Miro

BTW: if you ever recover the spreadsheet it would be most valuable to me and - I am sure - many other member of this forum
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Guy Croft
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Re: Differential ratios: Is this right ? CORRECTED

Post by Guy Croft » March 3rd, 2009, 11:01 am

Mick, hi

re: Firstly I don't quite espouse the notion that you should optimise gearchange points so you change up at peak power. I think you need to go past this as you will optimise the acceleration if you change up at the point where the engine power has decayed to the point on the power curve, where it equals the power you will achieve in the new gear.

Absolutely right. I just put the upchange at peak power on those graphs for simplicity.

Thanks anyway for drawing attention to that aspect.

GC

mickwood
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Re: Differential ratios: Is this right ? CORRECTED

Post by mickwood » March 5th, 2009, 6:23 pm

Hey Miro

At first sight it sounds like you have an impossible problem
You could optimise your car for your tracks (where it sounds like you are not going much faster than 150km/h tops)
....that would argue for the 7/43 diff (i would go for the CR box in any event if its within your budget, as you mentioned you were dropping right off the torque curve on upshifts)
....but then its going to be a real nightmare to drive any distance on the road
....but maybe you could put up with it you dont have to drive too far.

The only way to get best of both worlds is to have some way to change the gearing at the event _ I can only think of two ways of doing this

1) You mention the use of Abarth rear axle - if you can find another diff assembly (sadly not cheap) and make another subframe then you could build up two and swap them at the event - It can be done in about 30 mins on your own (once you have practiced it) and you can get it down under 10 mins with two (or max 3) of you if you apply some homework to making up Quick Release exhaust etc.

2) you could attack it through using a different set of wheels at the event. You could run really low profile slicks in the on the event on your existing 13" rims, and then have a higher profile set of tyres on 15" wheels for driving to and from the event (providing they dont foul bodywork). For example
205/40X 13 have a rolling diameter of cca 495mm
205/70x 15 have a rolling diameter of cca 668mm
A 35% difference (or equivalent to going from your 12/43 to a 9/43 0r 10/48)

The only problem is that either of these alternatives could work out costing you more than buying a second hand trailer!

M

miro-1980
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Re: Differential ratios: Is this right ? CORRECTED

Post by miro-1980 » March 6th, 2009, 9:14 pm

Mick,

It took me a while to chew on it.

Thanks for your explenation. I have really forgotten about the remaining variable - namely the wheels and tires...

As the Polish saying goes: no matter how you look at it your bud is always in the back.

Anyway, GC and others were suggesting exactly the same but I was not ready to accept the facts of life - looking to have both a race car and a street car in one.

As you say this is an impossible task to marry one and the other in one. And as someone put it: street car is no fun at a racetrack and race car is no fun in street traffic.

So the decision is final: 7/43 and a used trailer !

Thanks to you GC and all for the other forum mebers for their input !

Miro
www.131abarth.pl
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Mats
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Re: Differential (Diff) ratios

Post by Mats » May 28th, 2009, 8:04 pm

Lets not forget the efficiency loss when going to large numerical difference in a hypoid gear. 6:1 an up is almost a worm drive and is very inefficient. Around 3 is a good target, if you can't justify the cost for a close ratio gearbox you need to compromise of course. I'd say it's difficult to find a modern car that has over 3:1 ratio final drive.
But I wanted to add that just to get all the info on the table.
/Mats Strandberg

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