SMG to Manual
To some the SMG is the right gearbox – but to many a car such as the E46 M3 must be manual. Basically it’s a personal choice. Even the CSL, that only came as SMG, is known to be converted.
Actually the manual and SMG shares the same gearbox. The difference is that the SMG has a hydraulic shift – and no clutch pedal. The SMG is therefore not an automatic gearbox but a sequential gearbox where the electronics and hydraulics take care of the clutch and shift functions.
Here is a really fine video by Jamie's Garage and Jason from @ShopLifeTV. It shows all the steps and parts for the conversion from SMG to manual: Best Method to convert SMG to MANUAL in the E46 M3.
Improving final gear ratio
One relative simple way to improve the E46 M3 performance is to change the final (differential) gear ratio. From factory it came with the ratio 3,62 – meaning that the ingoing shaft (prop shaft) rotates 3,62 times faster than the outgoing.
If this ratio is increased, it will increase the torque delivered to the rear wheels – i.e. it will increase the force that pushes the car forward and the acceleration will be faster. At the same time the engine will rotate faster at any given read speed. The later means that the driver (if manual) has to shift gear a bit earlier.
There are 3 available final gear ratios: 3,62 (standard), 3,91 and 4,1. All these fit into the OEM standard LSD final drive (differential).
As far as I know the 4,1 was used in the E39 M5 and available in a Club Sport configuration. I am not aware where the 3,91 was used, but that too was an original GKN crown/pinion set. To my knowledge, there are no wear or other issues recorded to any of the 3 ratios. The known issues with the LSD clutch-pack (wear and play at right out axle) is another matter (see here) not related to the crown/pinion ratio.
It’s a bit difficult to determine precisely what the gains are when you change the final gear ratio. However, if we settle for a theoretical calculation with some simplifying assumptions, it can be done rather easily.
Let’s first determine the relation between engine speed and road speed. For that we need the circumference of the rear tires. This property you can find on the internet, example Tire Calculator (https://tiresize.com/calculator/ ). For the 255/35x19 the value is 208,16 cm = 2,0816 m. You have to stick to the SI Unit System in order for the formulas to work. The formula is:
Engine rotation [rpm] / gear ratio / final ratio x tire circumference [m] x 60 / 1000 = road speed [km/h]
The gear ratios are:
Calculating the formula and plotting the values (click to enlarge):
Please be aware, that the graph does not imply that the car can make over 300 km/h. The real achievable top speed depends on engine power, transmission losses, air resistance and if the gearing is optimized to deliver max power at exactly the possible top speed. This is seldom the case.
As you may see on the graph, changing final ratio from 3,62 to 4,1 increases the engine rpm approximately by 500 rpm when you compare same road speed.
In some cases it’s reported that this brings the car out of the drone region at normal road driving speeds.
It’s not possible to calculate the effect on top speed (provided the 250 km/h limiter is disengaged), however it seems likely, that the max top speed will drop from app. 275 km/h (171 mph) to app. 270 km/h (168 mph) when changing from 3,62 to 4.1.
Be aware that BMW speedo normally show 7 km/h too high. This is obviously a policy decision by BMW.
Now to traction force.
The traction force bringing the car forward determines how fast it will accelerate. By increasing the final gear ratio, the traction force increases (everything else equal). The practical traction force cannot be calculated. To establish this, the car needs to go on a dynamometer. However, to calculate the theoretical traction force is not difficult. The formula is:
Engine torque (Nm) x gear ratio x final ratio / rear wheel radius [m] = Traction Force [N]
The engine torque is:
Calculating the formula for a series of rpm and plotting the results against the corresponding road speeds we get this graph (click to enlarge):
As it can be seen 4.1 gives quite a bit more traction force especially in the low gears. In first gear it may even cause more wheel spin than you like.
Note that despite the calculations ignore transmission losses, they present a valid relative picture – i.e. the percentage increases will be the same in “real life”.
The standard E46 M3 (with 3,62) is informed to go 0-100 km/h in 5,1 s.
To calculate the 0- 100 km/h with 4,1, some approximations/simplifications have to be done. We have to assume that shifting gear take the same time regardless ratio – an evident assumption. Further it’s assumed that the transmission losses are the same and no wheel spin occurs in either case. Finally we assume that the traction force ratio is independent of revolutions/road speed.
With these assumptions Newton gives a helping hand:
Force = mass x acceleration (F = m x a)
Speed = acceleration x time (v = a x t)
If you use these for the two cases (1: 3,62 and 1: 4,1) you will end up with the following relation:
t(2) = t(1) x (F(1) / F(2)) or that the 0 -100 km/h time is inversely proportional to the traction force, which again are proportional to the final gear ratio (engine and gearbox being the same).
That means that the expected 0 – 100 time is: 5,1 x (3,62/4,1) = 4,5 s
4,5 s is pretty fast – not least considering that the CSL is informed to do it in 4,8 - 4,9 s.
Personally I like my 4.1 final ratio. It gives that little
extra punch that makes the car faster than quite a
few more modern “about 5 seconds cars” and, naturally,
most of the other E46 M3s. It’s also fun, that even if you
meet a CSL at the red light, you don’t need to be second.
Just an appetizer: Changing final gear ratio
BMW M3 E46 with 3.62 (Camera car and stock gear set) Topaz Blau
BMW M3 E46 with 4.10 (Middle) Silver Grey
BMW M3 E46 with 3.91 (Right) Titanium Silver
How to change the ratio is explained here: Differential
Some perspectives.
Strictly it is not correct to make the following simplifications, however it gives some interesting indications. The (main) errors in the reasoning relates to disregarding the inertia effects from rotating components such as crank shaft, fly wheel, clutch, gear wheels, prop shaft and wheels. In real life it takes quite a lot of torque to accelerate (spin up) these parts. To include this, however, one has to know weight and geometry of all rotating parts and calculate an equivalent mass to add to the car’s mass (weight).
So, disregarding rotating parts effect, here are some (rather correct) aspects:
The standard E46 M3 (coupe) weighs 1470 kg. How much weight reduction is needed to increase acceleration 0-100 km/h from 5.1 s (std.) to 4,5 s?
Using the above formulas, the answer is about 170 kg (or about 12%) – in reality probably quite a bit more due to the above simplifications - perhaps 250 kg.
To compare this, the CSL weighs 1284 kg – i.e. about 13% lighter than the standard M3. The CSL runs the same gearbox ratios and shares the differential. The CSL has a max torque of 370 Nm or 5 Nm (1,4 %) more than the “ordinary” M3. This increased torque cannot account for more than app. 0,1 s so the weight reduction of the CSL play a significant role.
Short Shift
Some M3 owners prefer a more “aggressive” gear shift, the so called “Short Shift”. The Short Shift is simply what it says, a short(er) shift, i.e. the gear lever knob moves a shorter distance when shifting than standard. Theoretically the Short Shift may reduce the time it takes to shift gear, but it’s probably more a feeling than an actual reduction of time. My guess is that you may gain in the vicinity of 3/100 sec. per shift.
As far as I know the Short Shift was an option,
but it surely was and is an accessory that can
be retrofitted.
The “price” for the shorter shift is that shifting
takes a bit more force.
The Short Shift is, of course, not an option for
SMG including CLS but only for manual gear.
The two pictures to the right show respectively
the standard shifter and the Short Shifter.
To get a Short Shift you only have to replace the
yellow marked items 4, 5 and 6. Note: Pos. Nos
are differs on the two pictures.
On the picture of the shifter lever the shown
distance is longer on the Short Shift.
In the table to the right you can see the part numbers
needed for retrofit, however it’s a good idea to
change possible worn parts too.
According to rumors it may be possible to convert to Short Shift by using parts from other BMW Models (E46 330d and e60 545i are mentioned) but I cannot verify this.
Other “Improving”
Some owners seek to improve their E46 M3 by replacing the “donut” (guibo) with a more “solid”. It may be needed for race, but for street use I will definitely recommend not to. The OE donut last quite long and being of a rubber composite it provides a needed damping of vibrations.
As a general rule harder bushes, dampers etc. increase stress, vibrations and noise – ie they are not improvements.
