I'm going through "Problem Solving, Abstraction, and Design Using C++" (Friedman, Koffman, 4th edition) and a programming assignment has me stumped. (I apologize for not knowing how to insert equation notation into this text). Chapter 3, project 11, begins:

"The ratio between successive speeds of a six-speed gearbox (assuming that the gears are evenly spaced to allow for whole teeth) is

5(nth power) square root of (M/m)

where M is the maximum speed in revolutions per minute and m is the minimum speed. Write a function that calculates this ratio for any maximum and minimum speeds."

Here's where my brain freeze takes effect. Assuming that you have a gearbox with 60, 50, 40, 30, 20, 10 teeth, driving a gear with ten teeth, the ratio between succesive speeds would be _different_ between each gear, yes? From top to bottom, it'd be 6/5, then 5/4, then 4/3, 3/2, and 2/1. But the text says that the ratio between successive speeds would be 5(nth power) square root of (60/10) or 6. How is that possible? What am I missing here?

TIA!!!

Attached Images

The ratio between successive speeds of a six.pdf (40.7 KB, 10 views)

You are missing the problem statement: it has nothing to do with gear ratio. It has to do with the maximum speed and the minimum speed for each gear selection. I don't know whether this calculation has any practical value, but that's not part of the problem.


The mathematical solution to the problem statement is the fifth root of M/m. The meaning of the symbol that looks like a square root sign but has a little 5 on is is "the fifth root of (M/m)" that is the same as (M/m) to the power (1/5)

So, I would make the Program Specification look something like this:


Regards,

Dave