# Zero-Loss Gearbox Analysis

## Introduction

My Zero-Loss Gearbox Analysis tool provides a means to visually compare the power curves of two engines with different operating speed ranges. As far as I know, this is an original concept. It works equally well for engines that peak at vastly different speeds (say 6000 and 12000 rpm) or two fairly similar speeds (say 6000 and 7000 rpm). I'd now like to share this method with the world. For demonstration, let's compare the Montesa 4RT and Montesa 315R. The actual spreadsheet is at the end of this page.

## Montesa 4RT versus 315R

Below is a dyno chart used by Montesa to tout the new, at the time, 4-stroke 4RT versus their 2-stroke 315R trials engine. Both displace approximately 250cc. Many people wish there were labels on the Y-axis for power and torque. But it does not matter for this comparison, as I will explain shortly. Elsewhere you can find claims that the 315R made 17.5 HP @ 5000 rpm and 19.2 lb-ft at 4000 rpm. Those values don't align exactly with this chart but are reasonably close. I've never ridden a 315R so can't comment on what the power delivery is like. However, the workshop manual for my 4RT 260 indicated the ignition timing is 45* BTDC at 10,000 rpm (which would certainly act as a rev limiter). The most I ever saw on my telltale tach was 9600 rpm. Let's assume the chart is reasonably representative of the WOT behavior of both engines.

2001 Montesa 315R was 72.2 x 61.0 mm = 249.7cc

2005 Montesa 4RT (first year for 4RT) was 76.5 x 54.2 mm = 249.1 cc

## Analysis

From the chart, it certainly seems like the 315R has a big advantage at low engine speeds – and it does.

But that can be overcome with the proper overall gearing.

Regardless of the motorsport we are considering, it's always the driving force at the rear wheel that matters

My Zero-Loss Gearbox Analysis tool uses a simple spreadsheet that starts with a dyno table (digitized dyno chart) giving rpm and horsepower for as many points as is feasible. It's most straightforward to pick the same rpm points (in this case every 500) from each chart as this obviates the need for interpolation.

These values are then numerically manipulated so that torque is traded for engine speed, and vice versa, in the same percentage. This maintains the horsepower but artificially forces the rpm range to be identical for both engines.

I normalize each dyno chart for a maximum engine speed of 10,000 rpm. This is just a convenient arbitrary value and any peak speed would work equally well. Alternatively, you can think of it as 0 to 100% of engine speed. The chart below is the result.

## Which is Better?

I'm used to seeing these charts but frankly, this one surprised me. The 4-stroke is better (makes more power) almost everywhere.

You may ask, what are the numbers on the Y-axis? Because power was not given in the original dyno chart, I just used inches. Yes, inches. I printed the dyno chart and then measured the height of the graph in inches with a digital caliper at 500-rpm intervals. The true power numbers are not important because both charts were printed at the same scale. It's the shape of the graph we care about (but only in comparison with another similarly-processed dyno graph).

Now, other factors can mitigate this picture somewhat. For example, the number of speeds in the gearbox (and how closely the ratios are spaced). But in this case, they are both 5-speeds. Another factor is part-throttle behavior. This representation (like almost all dyno charts) shows only what happens at WOT. This is fine for drag racing, but most other motorsports rely on part-throttle operation too. Similarly, it says nothing about driveability (aka throttle connection). Generally, 4-strokes are far more predictable than 2-strokes in this regard – although trials engines may be on more equal footing here. Of course, the weight of the engine is also a consideration. Coming to a determination as to which power plant is “better” must take all these, and other, factors into consideration. But that's not the point of this exercise.

## Real World Gearing

As can be seen, the 4RT's rev range is 125% (10,000 / 8000) of the 315R, but its gearing is roughly only 12% shorter (e.g., 36.27 / 32.35) in the “section” gears. For whatever reason, Montesa chose not to fully compensate for the difference. Perhaps this has something to do with 2-stroke versus 4-stroke? I know my 4RT was easier to stall than my OSSA. But there are a lot of other factors to consider, perhaps the most important is the inertia of the flywheel. The 4-stroke should require more inertia to compensate for firing only every other revolution.

It would be fun to ride the two bikes back to back now that I have made the comparison chart.

## Clarifying Remarks

The units on the spreadsheet column headings for torque should not be lb-ft. This is only correct if power is entered as horsepower. But because I measured power in “inches”, those units are meaningless here.

The final column “sanity check” just shows the original power value that was entered for each row. I put it in the initial version of the spreadsheet to check my arithmetic. It's no longer needed, but I never bothered to take it out.

Notice the starting point for the processed 315R graph. It does not extend as near to the origin as it could. However, that data would have to be extrapolated and I did not consider it very important. Think of it as a reminder that everything had to get “stretched” to make an 8000 rpm chart end at 10,000 rpm.

## The Magical Lossless Gearbox Explained

Recall that power is proportional to torque times engine speed. In Imperial units, that's:

horsepower = torque (lb-ft) * speed (rpm) / 5252

Imagine we have two engines that both peak at 100 horsepower – one at 6000 rpm and one at 12,000 rpm. By definition, the slow-running engine must make twice the torque of the fast-running engine. In this case, it's 87.53 lb-ft versus 43.76 lb-ft. If we had a magical lossless 2:1 gearbox at the output of the 12,000 rpm engine, we could slow it down to 6000 rpm. In doing so, the torque would double as the speed was cut in half.

We can apply the same thinking on a point-by-point basis using a spreadsheet and graph the results. Green cells indicate the data I entered. All other numbers are calculated.