Thank you.
what seems to be missing from these French calculations is the transmission set-ups.
You can get away with a lower powered engine
IF you have more gears in the transmission. But that means a more expensive, larger, heavier transmission. You can also go too far in this direction as the Germans did. You also need to make sure such a transmission is easy to shift (at least somewhat) and that the drivers are trained to know when to shift.
On the flip side the British (at least in cruiser tanks) used very high-powered engines (or at least high torque) that allowed the drivers to concentrate of driving instead of shifting.
Soviets used the high powered V-12 but the transmission was so poor that many drivers rarely got into high gear, meaning that the book/proving ground speed was rarely reached.
Also means that the fuel consumption numbers were never right.
For those of us that have driven manual transmission cars, not using high gear is going to affect fuel milage even if the engine itself is good for low g/hp/hour

Ease of shifting is important. Back in the mid 70s I had the
pleasure (not) of driving a fire truck with a poor engine swap and a crappy shift linkage. It had more power than the old engine and a lot more torque but it had a narrower rpm band, a crash box transmission (double clutching), a heavy flywheel, no accelerator pump on the carb and bent shifting rods in the transmission linkage. Truck also had manual (no power) steering which meant you had to do your shifting either before or after a turn, you did not have a 3rd hand to shift with while wresting the wheel.
If you blew a shift you had to stop the truck and start from 1st gear and standing start.
Perhaps there is another paper/study that concerns transmissions?
From the current knowledge of the archives, there is no overarching study on transmissions, but the ARL made a very detailed study with calculation notes on a mechanical transmission for the ARL heavy tank project of 1937 which was a 55-tonne vehicle powered by a 500 hp diesel engine meant to achieve a top speed of 30 kph, which was a challenging set of requirements compared to previous French tank projects. Link here:
AA 206 4H2 41 - ARL mechanical transmission - Google Drive
The ARL came up with a fully-mechanical synchronized preselector gearbox with 5 forward speeds (up to a theoretical 32.6 kph) and 2 reverse speeds (3 kph theoretical max, the 1st reverse being used for very low-speed maneuvering) coupled to a steering unit giving 3 steering radii per gear. Gear change was assisted and all the necessary actions were combined so that the driver would only have to use a gear-change lever and a steering wheel. This is rather in line with the most convenient transmissions of the time period and WW2 for the driver.
However the heavy tank project was turned into the even heavier fortification assault tank program which mandated electric transmissions, and this transmission type doesn't appear to have been further developped for lighter vehicles.
The ARL V1 75mm SPG used a Cotal preselector gearbox with 8 forward speeds for up to 42.6 kph theoretical (42 at least achieved in trials) and one reverse speed, mated to a Cotal steering unit with 2 steering radii per gear. This is analogous to Wilson-style transmissions, but with electromagnetic instead of hydraulic clutches. This didn't give any trouble in trials and made driving very easy. The clutch was of an automatic centrifugal type which protected the mechanical elements from jolts, comparing favourably with the SOMUA 75mm SPG with a conventional clutch which suffered from greater wear. An extrapolated form of this transmission was used in the ARL 44 tank. Last I checked, the transmission was already able to withstand the torque and power of the intended 340 hp-class engine.
The S35 used a 5 forward 1 reverse speed sliding mesh gearbox (pretty much the regular mechanical gearbox of interwar/early war tanks) mated to a double differential steering unit which made steering convenient and was on the progressive side much like the Merritt-Brown, Wilson and Tiger transmissions. Only the final drives had to be changed to use the 230 hp uprated engine from the S40. It was suggested that the S40 use a Kegresse Autoserve gearbox which was a form of automatic gearbox which simplified driver training and actions, eliminated driving errors and reduced mechanical wear. The steering unit could also get hydraulic assistance to further reduce effort but the main goal was to reduce the frequency of maintenance compared to the original steering clutches. If the S40 indeed entered production with this system, it would have been perfectly easy to drive and steer, but no information is available on the maximum input power or durability.
The B1 Ter featured a different gearbox from the B1 Bis (with 5 forward speeds as far as we know, described simply as:
Gearbox studied by the ARL and built by the BAUDET-DONON-ROUSSEL company. This gearbox was designed for the torque of the 300hp engine and was 22cm shorter than the B1 Bis gearbox, allowing a larger crew compartment.
This gain was obtained by :
- Using two secondary shafts
- Mounting some shafts on needle bearings
- Replacing some bevel gears with globular screws/globoid worm gears
While the engine was driving the primary shaft still in gear, the first secondary shaft ended by a globular screw was used for the first, second and third forward speeds and the reverse gear (with an intermediary shaft), the second secondary shaft was used for the third and fifth forward speeds and drove the main differential via a bevel gear. The planetaries and satellites were of the spur gear type as it was easier to build than conical/helical/bevel gears. The auxiliary differential driving the steering mechanism was driven by a globular screw.
This gearbox was also cheaper and lighter than the B1 Bis' type. The needle bearings were eventually replaced by roller bearings as they were deemed responsible for some failures during trials. It was recommended to add a 6th forward speed. Without further detail, I can not comment on how it compared to other mechanical gearboxes of the era. A full description exists in the 4th report related to question n°270 "Char B experiments" in the archives, but I have not read it yet.
With the appearance of the new Renault V12 engine, a new gearbox was designed to operate beyond the maximum 2000 input rpm of the original type and for an input power of up to 400 hp (420 hp V12 minus losses before the gearbox). By April 1940, it was reported that a gearbox designed for an input power of 480 hp was designed for a "modified B1 Ter" which was possibly the future ARL battle tank, also named the B40.
The B40 gearbox was described long after the war by engineer Lavirotte (who oversaw Char B and other tank development in the late 30s and 1940) as "gearbox studied by chief engineer Martin-Prével (director of the ARL), mounted transversely, containing 6 forward speeds and 6 reverse speeds thanks to a reverser, a main differential, an auxiliary differential, both using spur gears driven by worm screws." I can not comment on this type either, other than it enabled yet another reduction in engine bay length.
Char B gearboxes were mated to the Naeder hydrostatic steering unit, which was described by German engineer Kniepkamp as giving the following advantages and disadvantages:
Drawbacks: heavier, bulkier and more man-hours intensive to make than other types, and the tank can't be steered at "Mittelpunkt" (in place?).
Advantages: can provide all steering radii continuously and without losses, which reduces/eliminates heat, smoke and noise generation when steering, reduces wear, has no delay, doesn't require much driving effort, doesn't jolt/stutter, ensures safe driving even at high speeds and the steering direction doesn't suddenly invert.
I will add that it had lower efficiency than a purely mechanical system, just like torque converters. The B1 Ter introduced a simplified Naeder with the mobile parts being fully interchangeable. The "modified B1 Ter" further simplified it by
- replacing its belt drive system by a gear drive system from the gearbox
- removing the drive system for the Henry pump (now driven directly by the gearbox) which was made smaller
- deleting the entire front end of the Naeder which removed the delicate play of the generator shaft, the ball bearings being replaced by double conical bearings, set once and for all by the manufacturer instead of having to be reset periodically by the crew or maintenance units
- Improving cooling oil flow using an internal turbine
- improving the seals (the Naeder had a tendency to leak oil, which also clogged the radiators)
The B1 Bis/ unmodified Ter also were to use a Naeder belt tensioner to increase the life of the belt.
Aside from the improved and simplified Naeder, the other two options were:
- a Poniatowski-type electric steering unit which had greater efficiency and eliminated steering efforts, the Chobert radiator and reduced maintenance but had some quirks which made driving less convenient
- a THAV hydraulic unit studied by Baudet-Donon-Roussel since late 1937 which was more compact and less complicated than the Naeder. It eliminated the belt drive from the Naeder in the unmodified B1 Ter, which was desirable as this belt drive was inefficient and insufficiently durable.
The B1 Ters also tested servo assistance before the Armistice. Overall the Char Bs can be described as using a regular manual gearbox with a steering system which is easy to use, with a trend towards providing assistance to the driver's controls, simplifying the steering steering system and making it more reliable, and increasing the maximum input power. The next step would have been to use a preselector, planetary or automatic gearbox coupled with a non-hydrostatic steering unit providing the same advantages as the Naeder without the same drawbacks.
The Renaults G1R and DAC 1 used a seemingly regular gearbox with a controlled differential with Lockheed assistance (so one of the worst forms of steering).
The AMX light tank used manual 5-speed gearbox coupled to a controlled differential as the absolute backup, but the baseline were two Wilson preselector units with geared steering (so quite good for WW2), and the desired final transmission was the Robin Van Roggen automatic type, which would be upscaled for 45-tonne tanks if found successful on the light tank.
The British were good with Merritt-Brown and conservative before that. The Tiger units were very strong and convenient to use but complicated to make. The Soviets saw the problem with their gearboxes in 1940 and started working on 8-speed gearboxes (KV-1S and IS series) and planetary turning mechanisms (IS-1/2). Op Barbarossa delayed or cancelled some of these developments (T-34 with 8-speed or planetary transmission).