When reading about the latest drive train advances, authors refer to “Gear Inches” or sometimes just GI. If you are like me, you will skip over the magic numbers and attempt to understand the text alone. A concept of gear inches helps plan the changes needed to your trike to make climbing hills more pleasant.
How to Calculate
The formula for gear inches is simple and easy to calculate.
gi = rear_wheel_diameter_inches * (crank_chainring_teeth / rear_cassette_cog_teeth)
Most trike rear wheels are 20″ or 26″ diameter, including the tire. Usually, the rim is an ISO 406 (16″) for a 20″ wheel or ISO 559 (22″) for a 26″ wheel. If you use balloon tires, like Schwalbe Big Apple or Big Ben, then using 20″ and 26″ is pretty close.
As an aside, my favourite tire at the moment is the Schwalbe Big Ben. They give me good thorn protection, an excellent ride and a good grip on dirt. I run them at 20psi. The specification is 30psi, but we ride on three tires, not two, so 20psi gives a softer ride.
Since the rest of the formula includes the number of teeth on both the front crankset and rear cassette, we could calculate values for each gear. Fortunately, we only need two – the lowest (smallest front to largest rear) and the highest (largest front to smallest rear).
The result is a “magic” number called gear inches. We use it for comparison because the calculation is easy.
An Example Calculation
Model: Greenspeed Magnum BW
Tires: Schwalbe Big Apple (balloon)
Crank low gear: 30 teeth
Crank high gear: 50 teeth
Cassette low gear: 34 teeth
Cassette high gear: 11 teeth
gi_lo = 26 * (30 / 34) = 23
gi_hi = 26 * (50 / 11) = 118
What About Hub Gears?
The difference is minor, adding one variable.
gi = rear_wheel_diameter_inches * (crank_chainring_teeth / rear_sprocket_teeth) * hub_gear_ratio.
All the hub gears publish their minimum and maximum ratios. For example, a Nuvinci n360) (now from Enviolo) varies from 0.5 to 1.8. The Nuvinci on my Gekko fx uses a 22 tooth sprocket, so
gi_lo = 20 * (40 / 22) * 0.5 = 18
gi_hi = 20 * (60 / 22) * 1.8 = 98
The gear inches before exchanging derailleur for Nuvinci was 24″ to 92″.
Use the same approach for crankset replacements such as the Schlumpf drives. For their mountain drive the ratios would be 0.4 low and 1.0 high. Adding that to the ranges on the rear wheel can give a very low GI for climbing.
Theoretical Speed
Gear Inches provide almost all the data needed to calculate speed. Multiplying GI by the constant pi gives us the inches forward travel for each full rotation of the pedals.
How quickly we rotate the pedals is called cadence. Non-cyclists would call it rpm for revolutions per minute. A cadence of 60 (1 revolution per second) allows us to ride without premature tiring. There will be articles on finding your preferred cadence.
With the help of Wikipedia, a close approximation of speed is:
mph = gi * cadence / 336
kph = gi * cadence * 0.08
So, for my stock Magnum BW I could, in theory, ride it from 4mph/7kph in low gear to 18mph/29kph in high gear, all at a comfortable cadence of 60.
In practice, gravity, tire resistance against the road, wind resistance and mechanical resistance conspire to make the top speed and the best hill climb impossible at a cadence of 60. When that happens, we grind and suffer.
Climb Every Mountain?
Here’s the rub. Recumbent trikes and hills are not the greatest of friends. Getting off and pushing is not an easy option, while the recumbent position makes standing on the pedals impossible. Pedalling becomes painful long before the slope gets too steep. If the pain is muscular, it may limit how far you can ride. Excessive pressure on the knees can cause permanent damage.
As long as I have been riding recumbent tadpole trikes, I have felt that I should use the same amount of effort uphill or down. In a 2017 article in CyclingAbout, Alee Denham holds the same opinion. Making it work for a recumbent trike is another matter – and for another day.
Spoiler: We will estimate your chosen power setting by riding at a fixed cadence on a flat section of the road. From that, we can extrapolate the maximum slope you can ride with ease in your lowest gear. The next trick will be to calculate the gear inches needed to ride the hill you aspire to. Finally, we can find a gearing combination required.
Why Use High Gear Inches?
Gear systems have a limited range. As you lower the bottom gear to climb hills better, the top will drop also. If I swap the 30/40/50 standard crankset on my Magnum to a MTB 22/32/42, my top GI goes from 100 gear inches to 84.
You need to ride on the flat to your chosen energy usage without having to pedal too quickly. The article mentioned above will provide the required minimum top gear GI.
And then there is downhill. At what speed are you willing to coast and let gravity do the work? If I want a thrill, I might push my cadence to 120 until the Magnum reaches 36 mph (60 kph) before coasting. I am happy with drifting from 20 kph (13 mph) most of the time.
Conclusion
I hope this short article makes sense to you. It is central to the understanding needed when deciding what changes to make to your trike to make the best of your rides. Please comment below if anything is not clear. Thank you in advance.