## Thursday, January 23, 2014

### Ray's theory of hills

I have this idea, lets call it Ray's Theory of Hills.  My thought is that once balance is taken out of the equation, and assuming there is sufficient traction, the steepness of the hill that can be climbed is inversely proportional to the gear ratio expressed as gear-inches or meters development, and also inversely proportional to the total weight to be propelled up the hill, including trike and riders.  (This is basically a statement about torque and not horsepower.  We're not talking about racing up hills.  The claim is that your own weight, converted to torque, must be greater than the weight of the cycle and everything in/on it.)

So, you want to take a trike up a hill that is 50% steeper?  Loose 33% of the mass, or lower your gear-inches by 33%.  Or, want to carry 50% more junk?  Lower your gear-inches by 33%, or slopes by 33%.

What does 33% of the mass of a loaded trike add up to, anyway?  So lets say 35kg of Nihola, 75kg of driver, 40kg of kids and 15kg of stuff for a total of 165kg, of which 33% is 55kg.  So by removing all kids and stuff, the same trike and driver could theoretically climb a hill that is 50% steeper (so a 15% slope instead of 10%).  Or put another way, adding the kids and stuff reduces the maximum slope by 33% (so a 10% slope instead of 15%).

Or here's a fun one.  How about removing 10kg from the steel trike by making it an aluminum bike (i.e. swap the Nihola for a Bullitt).  Using the same cargo, that should boost hill climbing potential by 165/155 = 6%, so a 10.6% slope instead of 10%.  This is essentially nothing, of course, and the fact is that freedom from balancing is powerful at low speeds.  For these two reasons, I consider even the sporty Bullitt to be a poor choice for moving kids on steep hills.

(Of course I would buy a Bullitt to find out, if I could justify the expense.)

Consider the effect of carrying just one child, lets say 15kg of kid, no cargo, 75kg rider and 35kg of Nihola for 125kg.  Compared to the empty trike, this only harms climbing by 110/125 = 12%, so if you could climb 15% empty you can climb 13% with the kid.  I've often been surprised when I try to race up a hill with a "lightweight" empty Nihola, because I can't go nearly as fast as I feel like I should be able to.  The 15kg kid makes less than a single gear of difference.