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CHOOSING GEAR RATIOS For Best Performance - CF-301

On 16 December 2009, Juan Gil Gutierrez in France wrote:
>>"As I had a 4.3 ratio in my differential, the original one, I though that the 'always running short' feeling was due to it".

My MGA ran the first 315,000 miles with 4.300:1 final drive. I finally changed it to 3.909:1 in 2002, shortly after uprating the engine a bit, as it would then run past red line in top gear.

One interesting thing about the lower gearing is that I sort of expected it to make the engine run slower. But what actually happened is the car now runs comfortably faster on the expressway with about the same throttle and engine speed, so now I spend more time in the fast lane rolling along with whatever vehicle is making good progress. You should keep in mind though that lower gearing does not make the car go faster at top speed, as that is a function of maximum power available. If you over gear it the engine will not have enough torque to achieve top speed, and you would need to catch a lower gear to run faster (especially for climbing hills).

>>"The matter is I'm not sure about the new differential ratio I'm going to install in her. I've read all what you wrote about and talked to a specialized local dealer. They first suggested me the MGA MK-II 4.1 ratio. They said that I will loose just a little down and gain just a little in speed terms. When I asked them about the early MGB 3.9 ratio they first doubt it concerned about me loosing so much acceleration but then, when I asked them if I was right considering my overpowered MGA as a sort of MGB with overdrive (because of my 5th gear) they agree with me. So, will it be right to set the 3.9 ratio in my MGA?. Will I really loose something considering that we were driving too short or will I gain comfort and speed with not that much loose of torque"?

This depends on how much torque you have available at the crankshaft. As engine speed decreases with overdrive gearing, the engine torque may actually increase a bit, but the propshaft torque decreases proportionally with the gearing change. At some point the propshaft torque may not be sufficient to drive the car into the wind at normal highway speed, which is when you know you over did it.

As originally built the cars were geared to run at highest possible top speed at the point of peak power output of the engine. You need to look at the torque and horsepower curves to determine the best gear ratio for top speed. The idea is to figure out how fast the car can go with the power available, then select a final drive ratio that will make the engine run at the peak of the power curve at that road speed. If you get it wrong, the engine may run past red line at high speed (over-revving), or it may not have enough torque at the propshaft to achieve best speed (lugging down). In the later case it doesn't pull hills or push into a strong headwind very well.

The MGA 1600-MK-II (about 87 hp) had top speed around 103 mph at 5650 rpm with the 4.1 final drive. My warmed over 1625cc engine with big valve head and fast street cam may be close to 100 bhp. It can do at least 105 mph at 5600 rpm. In other words, it is the perfect final drive ratio for attaining top speed. If not for the unjustifiable cost, I would be delighted to have a 5-speed gearbox with a nice overdrive ratio to run the engine slower for normal highway speed cruising. The engine does have enough torque to pull a tall OD ratio above 90 mph on the level. For passing or hill climbing or top speed I could always drop it back to direct drive 4th gear to let it rev up higher for peak power output.

>>Am I right when I say that in case I put the 3.9, and the car goes down in a noticeable way, I could always perform it to compensate the power loss"?

That may have lost something in the translation (I don't understand), but I'll give it a shot anyway. Hang on while I ramble.

Smaller final drive ratio makes the propshaft run slower in relation to the rear wheels. When the engine runs slower in 1st gear it will lose a bit on acceleration from a standing start up to the speed where you would originally have to shift into 2nd gear. For the MGA with standard gearbox and 4.3 final drive that would be 28 MPH at 6000 rpm in 1st gear.

If you want to rocket off the starting line with a little tire spin, acceleration is limited by tire traction anyway, so the final drive ratio does not affect initial acceleration up to about 15 mph (3200 rpm) when the tires stop spinning and it "digs in". That leaves a speed range about 15-28 mph where you have perhaps 10% lower acceleration rate with 3.9 final drive vs 4.3. If you are going to a lower final drive ratio, It is rather presumed that you have already warmed the engine over enough to make up the difference in acceleration with more engine torque. In that case acceleration within that speed range may be similar to original issue. In other words, if you get the final drive gearing right to go with available engine torque, it will make very little difference in acceleration up to 28 mph.

With a 10% change in gearing your 6000 rpm 1-2 shift point changes from 28 mph to 31 mph, so you can keep it in 1st gear that much longer. This improves acceleration (by about 60%) in that speed range when you don't have to catch a higher gear to prevent over-revving. Once you stick it into 2nd gear you're back to the balance and compromise between improved engine torque and decreased final drive ratio, and acceleration may be about the same as original from 31 mph upward.

When you hit red line in 2nd gear the scenario repeats. Rather than making the 2-3 shift at 46 mph you can push it up to 50 mph with the same 6000 rpm engine speed. This gives you better acceleration (again about 60% better) in the 46-50 mph range by using the lower 2nd gear ratio. After the 2-3 shift you're once again back to the balance between better engine torque and lower final drive ratio, and acceleration is closer to original issue.

By now you should know what's coming next. When you hit red line in 3nd gear the scenario repeats. Rather than making the 3-4 shift at 74 mph you can push it up to 82 mph with the same 6000 rpm engine speed. This gives you better acceleration (about 37% better) in the 74-82 mph range by using the lower 3nd gear ratio. After the 3-4 shift you're once again back to the balance between better engine torque and lower final drive ratio, and acceleration is closer to original issue, until you hit top speed or red line, whichever comes first. Difference here is that top speed is going to be somewhat higher than original thanks to the increased engine power.

If you have followed through all this carefully, you notice these differences:
15-28 mph = 10% reduced acceleration (augmented by xx% increase of engine torque)
28-31 mph = 60% improved acceleration
46-50 mph = 60% improved acceleration
74-82 mph = 37% improved acceleration
91-??? mph = improved top speed

This last line depends on how much power you have in the engine. The 1500 originally had top speed of 91mph with 4.3 gearing. The 1600 could do about 97 mph with 4.3 gearing. The 1622 could do 103 mph with 4.1 gearing. My 1625 with a little cam upgrade can do 105 mph with 3.9 gearing. The 1800 with similar cam upgrade might do close to 111-112 mph at 5900-6000 rpm. If you manage to have more than 110 BHP in the engine, then you need lower final drive gearing for top speed without running past the red line.

You should have noticed that I didn't mention overdrive yet. If you have lots more power in the engine you might get higher top speed with an overdrive gear. You must be conservative here though, as 5th gear or an overdrive commonly give around 0.800 to 0.700 reduction ratio. Taking the reciprocal of those numbers, 1.25-1.43 gives you the amount of increase in engine torque that would be required just to pull the same top speed with the engine running that much slower. You may rest assured that you will most likely never get 137-157 BHP (at 6000 rpm peak) from the 1800 engine in streetable form. That means it will go faster in 4th gear than it will in 5th gear due to insufficient torque to pull to top speed in 5th gear. This is not really a problem though, as you can always shift back to 4th for acceleration or top speed or hill climbing. The real issue is not to over-gear it so high that it will not pull normal highway speed on the level into a slight head wind in 5th gear.

Another solution to this might be to install a supercharger to increase engine torque by 30%-50% at similar engine speed. Otherwise you need a more powerful engine (larger displacement) to pull speeds much higher than about 115 mph with any gearing. Power requirement generally increases as the square of ground speed, so 30% increase of engine torque (supercharger) could get your 1800 up to about 125 mph. Keeping that under 6000 rpm would require 3.500 overall final drive ratio, or 4.300:1 rear axle combined with 0.800:1 fifth gear or overdrive.

3.91 rear axle and 0.8 fifth gear would match 6000 rpm to 140 mph (if you had about 175 BHP to get there).

This is not necessarily a question of how much power you need to achieve what top speed you have in mind. What you really want to know is how slow can you run the engine when doing normal highway cruising speed? Here the solution lies with inspection of the engine torque curve, and comparing that to the rear wheel torque required for the speed you wish to travel. Another issue is not to run the engine so slow that it falls off the torque curve and gets bad fuel economy. See below a Power vs. Speed curve from a test report on a stock 1956 MGA 1500 (from Motor Road Test 23/55 Continental). This curve is for direct drive 4th gear only with 4.3 final drive ratio. Notice where power required crosses power available, top speed is 97 mph.

When you see a power curve for an engine alone, it will commonly include a torque curve. The torque curve is a shallow camel hump with peak around 3500 rpm, falling off slowly thereafter, then falling off rapidly after about 5000 rpm due to flow restrictions with intake and exhaust tracts. Horsepower is a product (multiplier) of torque and speed, so the power continues to increase at higher speeds in spite of slightly declining torque. It is the severe torque drop off at high speed that ultimately kills the power curve. A hot camshaft moves the torque curve slightly higher with torque peak at somewhat higher engine speed, and the severe drop-of point also at higher engine speed, so it revs better and produces more power near the red line (with less torque at very low speed). When thinking about slowing the engine down with overdrive, you might like more torque at lower speed, so a hot cam is not necessarily beneficial for this cause.

An engine will have best thermal efficiency when running near the underside of the torque curve. This means it likes to be loaded up and running near full throttle, as long a there is useful work to do with the power available. This is why a small displacement engine may give better fuel economy than a larger engine. As the smaller engine "works harder" it is running at higher throttle closer to the limits of the torque curve. It is higher cylinder pressure that makes it more efficient.

One way to improve fuel efficiency is to slow the engine down with gearing mods so it has to produce more torque at lower speed to give same power output at a given cruising speed. (Slower engine speed also reduces "pumping loss" slightly, but that's a separate issue). The limit to this progression is if you gear it down so much that torque required will be higher than torque available in the engine, in which case you're screwed because the engine will not pull it.

Power required to make a car cruise down the road is a function of rolling resistance, wind resistance, head winds, moderate up hill grades, and a little friction in the drive train. All of this is independent of the engine and gearing. So it is possible to determine (calculate or test) the power required to drive at any given speed. For the purpose of selecting a final drive ratio for overdrive 5th gear, you first need to decide how fast you normally want to cruise in 5th gear with a bit of a head wind and a little up hill grade. Then you take the power required for that task and compare it to the power curve for your engine. Follow the power curve downward to the left until you get down to an engine speed where the power available is equal to the power needed for cruising at the desired road speed. Then install gearing, including overdrive 5th gear and final drive gears (multiplied together) to make the engine run at this desired speed, or slightly faster (but definitely not slower).

Having done this you will be able to cruise at desired road speed in 5th gear with lowest possible engine speed and best possible fuel economy. If you need more rear axle torque for hill climbing or swift passing you can grab a lower gear in the transmission to let the engine run faster to produce more power (and more torque on the propshaft). If you want highest top speed, drop it into direct drive 4th gear and let it rip, right up to 5500-6000 rpm for max power. The trick to this combination is to select the rear axle final drive ratio for best top speed in 4th gear, followed by selecting a 5th gear overdrive ratio for lowest engine speed (considering available engine torque) and best fuel economy while cruising.

There is another consideration in selecting the overall gear ratio for cruising. When running near the underside of the torque curve, you might like the running point to be slightly to the right of the hump on the torque curve. Then when you hit a head wind or a mild hill that will slow you down a bit, as the car slows down a little the available torque increases to handle the increased demand. If you can tolerate this slight speed reduction you don't have to downshift right away, and you may not even need to press the gas pedal any farther down.

On the other hand, you may realize that your MG 1800 will have more power and torque than it needs for cruising at moderate highway speed. So you can gear it down more to slow the engine down, moving the running point to the left but still below the torque curve. If you get this point too close to the left bank of the torque curve, then when the car encounters a slightly higher load demand it will "stall out" and begin losing speed dramatically. To avoid this you can run left of the peak on the torque curve, but allow some head room between your nominal cruising point and the underside of the curve. Then when the car encounters an increasing torque demand you can press the throttle down to gain a little more engine torque without having to downshift. This is in essence what a cruise control unit does. The limit here is when the load demand exceeds available torque at full throttle, in which case you have to catch a lower gear.

For many years when I was running a stock 1500 engine with 4.3 differential, I avoided reducing the final drive ratio, because I towed a trailer a lot and had to shift down to 3rd gear in the truck lane for climbing moderately steep grades on expressways (around 60 mph). After I installed the warmed over 1600 with close to 100 BHP I could climb the same hills with the trailer at 70 MPH in 4th gear. But then without the trailer it would run past red line in top gear if I stood on it long enough, so that was when I finally changed the final drive to 3.9. I can still negotiate most moderate grades in 4th gear with the trailer. This is independent of any decision to install a 5th gear with overdrive ratio. If I hit a hill with the trailer and overdrive, I can still shift down to 4th gear and cruise on up the hill as before. After cresting the hill it would be back to 5th gear for long distance cruising.

The only reason I don't install a 5-speed is cost, and very little return in fuel savings (not cost justified). But someone driving a lot at cruise speed on the highways may appreciate the slower engine speed (quieter running) enough to pay the piper for the 5-speed upgrade. Lots of people do. There are plenty of MGB running with stock engines and factory overdrive units.

5th gear in the Ford Type-9 gearbox is usually 0.82. MGB OD units are mostly 0.802 ratio, except very late production at 0.820. These are standard MGB setup with 3.9 final drive and 14-inch tires, and anyone can tell you that these engines could pull an even lower overdrive ratio. Running your MGA with 3.9 final drive, 0.80 overdrive, and 15-inch tires is just as easy. The difference in diameter of 15 vs 14 inch tires, is about 26/25, or only 4% change of engine speed. This would be equivalent to running 3.75 final drive ratio in the MGB with 14 inch tires. If I felt rich enough to spring for a 5-speed I think I'd be looking for a taller overdrive ratio, somewhere around 0.72 or even 0.67, in combination with the 3.9 final drive. For what it's worth, there have been a couple of Audi 6-speed gearboxes installed in MGBs (with direct drive 4th and two overdrive gears).

So go ahead and install the 3.9 final drive first, and see how you like it. It is a very cheap swap compared to cost of a 5th gear (especially if you need to replace the differential anyway). Then if you want to spring for a 5-speed, don't be afraid of low overdrive ratios. The OD gear is only for cruising at steady and moderate speed. You will always have 4th gear available for acceleration, hills, or top speed runs.

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