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What differential ratio is needed?

PostPosted: Sun Nov 05, 2006 11:08 pm
by msd1107
There have been questions as what final drive ratio is necessary under some conditions. This post addresses what final drive ratio is necessary for top speed. Other questions pertaining to gearing for race conditions are best addressed in a different post.

The question of what R&P may be needed is dependent on the car, engine power, and tire size. As opposed to the original Elite that was designed to a rather high theoretical standard, the Elan is very much a car of compromise, and was substantially under geared in all configurations produced.

For instance, the original Elan was geared for 90 mph on 145-13 tires, 3.9 R&P, and 95hp at 5,500 as introduced, although it would easily pass 6,000. Contemporary road tests either ran up to the 6,500 rev limiter, or to 7,000 with the fastest being 128 mph on 155-13 tires, 3.55 R&P, and a [email protected],000 SE engine (at which speed the engine was probably barely producing 100hp).

Often, a car is geared so that maximum speed is achieved at over, but close to, the peak power RPM. The tables below will give a sampling of what could be top speeds achievable for various configurations of engines, and the closest R&P to go with different tires to achieve that speed. The RPM chosen is 200 over the power peak. (For those who want to experiment more, I have a spreadsheet that eases this what if scenario considerably. Enter tire info, engine RPM info, R&P, and gearbox ratios, and it generates enough tables and graphs to satisfy the most extreme figure maven.)

Note that the calculated figures will be for a FHC, a DHC will be slower due to the poorer CD of the convertible top. Speeds will be slower if you run large side view mirrors, engine driven fan, wide tires, flares, etc. Speeds will be faster if: You do not have side view mirrors. No engine driven fan. Use narrow tires and no flares. Fair in the windshield. Go to a nose mounted scirocco or other nose mounted aluminum radiator. Use an electric water pump. Install 036B 1145 as per page K9 of the workshop manual. Improve the air venting from the engine compartment as per page K10 of the workshop manual or other methods to vent air from the engine compartment.

Common tire sizes are 155-13, 165-13, 185/70-13, 185/60-13 and the Spyder (Minilite) 185/60-14. Engines will be 95 at 5,500 (standard or Stromberg), 115 at 6,000 (SE), 126 at 6,500 (Sprint Big Valve), 160 at 7,000 (well modified road engine) and 240 at 8,200 (BD series 2.0L).

......................Calc.................diff ratios for various tire sizes
.......................top
.HP......RPM speed 155-13..165-13..185/70-1..185/60-13..185/60-14
095 at 5,500..123....3.03......3.11.........3.09..........2.89...........3.02
115 at 6,000..131....3.09 .....3.18.........3.16..........2.95...........3.08
126 at 6,500..136....3.24......3.33.........3.30..........3.09...........3.23
160 at 7,000..147....3.22......3.31.........3.28..........3.07...........3.21
240 at 8,200..168....3.28......3.37.........3.35..........3.13...........3.27

Interesting, eh? Shows we have been running around in virtual 3rd gear all the time. And a well modified Elan is a modern day 150 mph car.

But look at the speeds in 1st gear. Even with the 2.97 wide ratio (which should be pitched over the first cliff and replaced with the proper 2.51 set) you get 41, 44, 46, 50, and 57 for the different horsepower figures. With the 2.51 1st gear, you get 49, 52, 54, 59, and 67 for the different horsepower figures. Now, I have run a 2.51 1st with 3.55 and 165-13s, and it is possible although challenging in San Francisco, but I think few others would like to do so. (I also ran a motorcycle with a 5 speed with a 1.9 1st, over 60 mph in 1st, that was challenging also)

What are remotely achievable R&P ratios? Well, there were pinion gears with 7, 9, and 11 teeth. And ring gears with 31, 32, 34, 37, 39, 41, and 43 teeth. 11:31 is 2.82, 11:32 is 2.91, 11:34 is 3.09, 11:37 is 3.36, and it goes away from there. Does any one know if the 11 tooth pinion can be mated with the smaller ring gears?

Obviously, we need a 5 or 6 speed transmission. Comments are gratefully accepted. My personal email is david_harralson at hotmail.

Re: What differential ratio is needed?

PostPosted: Sun Nov 05, 2006 11:54 pm
by Dave-M
Sounds like we need to fit a 12,000 rpm 160 BHP sequential 6 speed Bike engine and box.
Regards
Dave

Re: What differential ratio is needed?

PostPosted: Mon Nov 06, 2006 1:08 am
by msd1107
Dave,

That is a good approach. A side benefit is that it saves a couple of hundred pounds.

Although it hasn't been done in a front engined car, Quaife has a differential to adapt bike engines. There would be some technical issues in bringing the chain drive down the length of the transmission tunnel, idler sproket mounting, supporting, and spacing, etc. Serious weight saving measures could bring the all up weight under 1100 lbs, making for an excitingly accelerating car.

David
1968 36/7988

Re: What differential ratio is needed?

PostPosted: Mon Nov 06, 2006 8:28 am
by Dave-M
David,
My reply was light hearted but It is quite a common thing to do in the Kit car world, particularly in Lotus 7 replicas The engine is turned through 90 degrees and the propshaft is bolted to an adaptor fitted to the gearbox output shaft. One of the biggest problems is that the engine needs a dry sump system to operate correctly.
Might be just the job in a baby elan
Regards
Dave

Re: What differential ratio is needed?

PostPosted: Mon Nov 06, 2006 10:36 am
by steveww
If you gear the car the high speed low rpm you will loose some of the acceleration.

I think fitting a 5 speed (type 9) gear box is the best solution and a number of solutions are available based on this idea.

Re: What differential ratio is needed?

PostPosted: Tue Nov 07, 2006 1:07 am
by christoph
Dave-M wrote:Sounds like we need to fit a 12,000 rpm 160 BHP sequential 6 speed Bike engine and box.
Regards
Dave

Are, would you believe it, my first post and I might know something about this.

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it's a Suzuki HAYABUSA turbo 300/ 400 and more bhp (1300cc- 72kg including 6 speed sequential box) 500kg, 0-100 mph 6.7 sec 160mph max or there about ,biult by me. No plans to pop it in to the S4 but it could go in this though
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:) Thanks for a very helpful forum
Chris.

Re: What differential ratio is needed?

PostPosted: Tue Nov 07, 2006 8:24 am
by rgh0
David

I think your calculated top speeds are a little optimistic.

My Elan which is a standard body shell S4 FHC with just one small side mirror and has 135hp at rear wheels on the dyno or around 170hp at the flywheel at 7500 rpm. With its 3.77 diff it will pull 7500 to 8000 rpm depending on the day, down the main straight at Phillip Island which is slightly down hill. This is just over the power peak and on Yoko A032R 175/60 x 13 with a rolling radius of 262mm this equates to 200 to 210 km/h or around 125 to 130 mph.

Using Hoosier 185/60 x 13 Street TD tyres which have a rolling radius of around 245mm it will just reach the rev limiter at 8300 rpm on the same track which is 203 km/h or 126 mph.

You may get a little more with a strong tail wind on a very long straight but 147 mph for a 160hp car sounds not achievable.

regards
Rohan

Re: What differential ratio is needed?

PostPosted: Tue Nov 07, 2006 6:32 pm
by msd1107
Hi Rohan,

Thanks for the figures. I am used to using tire rev/mile as this figure is often supplied by the tire manufacturers, and is some what more precise than rolling diameter or radius. The Hoosier figure seems small for a 185/60-13, are they shaved?

Lotus homologated a 3.44 R&P, ostensibly because long distance racers needed to keep their revs under 7,000. With the tall racing tires of the era (Lotus did their figures based on something like 820 tire rev per mile), this was a pretty formidable speed.

I use a spreadsheet that does all these calculations, and allows for easy changes. I would be happy to email you a copy if you wish (I am at david_harralson at hotmail dot com).

The table was generated from published road test reports to establish a base figure. Most road tests ran out of revs or on the rev limiter. So the test that used a 67 S3 SE with 155-13, 3.55 and ostensibly [email protected],000 got the base value I used at 128 at 7,000 (Theoretical 130, so some tire slip or other factors.) It does not appear the engine was tweaked for the test since the acceleration figures correlated well with 105-110 HP. The other figures were derived from cubic extrapolation.

My personal experience is some what limited. My bog stock '69 S4 SE Stromberg with 3.77 and 165-13 got to almost 7,000 after its 36,000 tuneup, which is over 200KPH. And my current car with 3.55 has seen easy bursts over 6,000, but I have never taken it to a proper timed facility.

Cheers,

David
1968 36/7988

Re: What differential ratio is needed?

PostPosted: Tue Nov 07, 2006 6:43 pm
by elansprint71
Chris,
It is very strongly recommended that you do not lift an Elan body anywhere except along the sills between the wheelarches, because the tail section, in particular, is prone to cracking above the centre of the wheelarch, oops, looks like you may aready know that. :twisted:

Cheers,
Pete.

Re: What differential ratio is needed?

PostPosted: Tue Nov 07, 2006 7:10 pm
by steveww
You will have to wait until the spring for GPS readings, however my S4 easily hits the 6500 rev limiter in top with a 3.77 diff and 155x13 tyres. No idea what speed this happens at but if feels rather quick :shock:

speed at 6,500, 3.77, 155-13

PostPosted: Tue Nov 07, 2006 9:54 pm
by msd1107
Steve,

That configuration gives 113-114 mph.

I have a spreadsheet that lets you get all that information, including charts and graphs for any setup you want. I'll email you a copy if you want. I am at david_harralson at hotmail dot com.

David
1968 36/7988

Re: What differential ratio is needed?

PostPosted: Wed Nov 08, 2006 9:38 am
by christoph
elansprint71 wrote:Chris,
It is very strongly recommended that you do not lift an Elan body anywhere except along the sills between the wheelarches, because the tail section, in particular, is prone to cracking above the centre of the wheelarch, oops, looks like you may aready know that. :twisted:

Cheers,
Pete.

Hi Pete, thanks for the info, but the body has already got some pretty heavy crazing and cracks on the OS arch + what you can see in the pic. The body is now striped of paint, sitting on a trolley awaiting some TLC and a zillion hours of prep :) . Chris.

Re: What differential ratio is needed?

PostPosted: Fri Nov 10, 2006 2:38 am
by 1964 S1
Hi Chris, I'd follow Pete's advice anytime the body is lifted. Cracks can reappear, and lengthen...
...and er, sorry ...
about gear ratios and bike engines. As silly as it sounds, on Playstation's Gran Turismo I have a racing Elan and have experimented with ratios. I know it sounds nuts but my results are very similar to what David, and, Rohan state. I'm not sure what a guy would have to do to get a stock bodied 1558cc to 150 mph and I'm also sure I wouldn't want to drive it (that fast.) Are there land speed records based on wheelbase?
If I were to put a bike engine in an Elan, I'd choose a shaft drive model.
Eric

Re: What differential ratio is needed?

PostPosted: Fri Nov 10, 2006 7:45 pm
by christoph
If I were to put a bike engine in an Elan, I'd choose a shaft drive model.
Eric[/quote]

Hi Eric, I was only joking about popping a bike engine in my Elan, but if any one did fancy it, I would not limit the choice to shaft drive bikes. Most bike engine cars employ shaft adaptors from the sprocket output shaft, + benefit for in line fours is north south orientation.
If one had the budget, it would be good fun to take a few scalps at the track though :). Here in the UK, I know of an Elise and a Golf both of which have 400bhp turbo Hayabusas fitted :roll:. All though hardly the remit of this forum, I'd be more than happy to advise, if someone wants attempt a turbo Busa install :wink: :lol:
Chris.

Re: What differential ratio is needed?

PostPosted: Fri Nov 10, 2006 8:58 pm
by Dave-M
Christoph,
Fabulous seven installation, looks superbly engineered.
Just for the sake of discussion, if a bike engine were to be fitted in an Elan, how would you overcome the excessive propshaft length required? As the engine would have to fit in the same position as the twink or further forward the propshaft would have to be it's existing length plus gearbox length, ie around 6 foot in length. I suspect it would be too long to operate correctly/safely. Fitting even a 200 BHP bike engine sounds superb how do you think it would go for day to day driving?
Regards
Dave