Help calculating differences with changing cogs
 

I need a little help calculating differences with changing cogs and the increase in speed on my recumbent trike. I'm trying to use a phone app and not sure if it's correct. What I'm looking at is if I change my rear cog from a 20t to 16t the increase in speed. Specs... chainring 42t (170mm arms) 20t cog (current) 20x1.75 tires I get 15.2 mph max with my cadence. The app says 19.1 mph with a 16t. Does this sound about right?

Thanks!

Let's start at the beginning so you'll understand this better. There's a piece of data missing with the numbers you provided.

First, you need to understand the concept of "gear inches". Gear inches (also called development), is how far the bike will travel with each revolution of the pedals. The distance varies based on the following formula:

gear inches = wheel diameter * teeth in front chainring / teeth in rear sprocket

So, given your 20t setup, you would have 20 inches * 42t/20t = 42 gear inches

On edit:
This means that for each revolution of the pedals (in those gears), the bike will move forward 42 inches times pi (use the circumference of the wheel (pi * d)).

Now, changing the 20t sprocket to 16t, you would have 20 inches * 42t/16t = 52.5 gear inches

This means that changing from the 20t sprocket to the 16t sprocket, for each revolution of the pedals you would travel 10.5 inches times pi further.

When you add the element of speed to the discussion, you have to know your cadence which is the rate at which your are spinning the pedals. Given your app's statement that you would be traveling at 15.2 mph (it has to know your cadence to provide this information), changing from the 20t to the 16t sprocket would yield a speed of 15.2 * 52.5 gear inches / 42 gear inches. This would yield 19 mph. This means that making the switch, if you maintain the same cadence, would increase your speed from 15.2 to 19 mph.

You cannot convert gear ratios to speed without considering cadence. Without extra effort, you would not see any increase in speed at all. Going from 20t to 16t, without extra effort, will increase your distance per pedal revolution (i.e. gear inches) but it would correspondingly decrease your cadence because it would be harder to pedal.

By the way, there are more things to consider when changing a single sprocket. You should also consider the jumps between the next higher and lower gears. There's something to be said for keeping a consistent relationship from one gear to the next.

Hope this helps.

the faster you pedal (cadence), the faster you go, no matter the gearing. you need to decide what cadence is max for you. they vary from individual to individual, a lot :). and there is a time interval involved in your 'max' to consider too.

Plug in your numbers and let someone else do the math:

Mike Sherman's Bicycle Gear Calculator

If you can maintain the same cadence with the higher gearing the speed is relevant. On a recumbent, you are fighting less wind resistance than most cyclists, so it could be doable.

However, it sounds like you are riding a single speed, you need to remember that the smaller cog will make starting from a stand still (or accelerating from low speed) more difficult, and also any hill climbing could be more difficult.

Thanks for supplying the formula, I found the result from Sheldon Brown's site after posting but will remember how to work it now.
Yes I'm riding a recumbent and with a internal hub (Nuvinci N360) and I think I'll not have a problem maintaining my cadence since when I max out my speed I spin out as well... like I'm looking for more overdrive.

This was an unknown while I was riding(I never counted), while I was using the android app I used the known data I had from the cheap meter: Max speed (15.2), and from the hardware specs: wheel(20x1.75),crank size(170mm),chainring(42t),cog(20t) and with this entered in the app the slider for cadence I moved until my speed showed 15.2 and this is where I got cadence. I'm not sure that worked like that but when I changed the cog to 16t from 20t I got 19.1 mph.

Use Sheldon Browns calculator

Sheldon Brown's Bicycle Gear Calculator

You guys are making this too hard. If the cog is changed from 20t to 16t and everything else, including the cadence, stays the same, the speed goes up by the ratio of the teeth: 20t/16t = 5/4. 5/4 x 15.2mph = 19.0 mph.

- Ed

not quite right regarding development
 

But close.

Gear inches refers to the wheel diameter you would have if you were riding a penny farthing.

Development...distance traveled, is gear inches times pi.

assume a 700x25tire...

So, 26.4x 42÷16x3.1416= =217.71288inches traveled.

/12x60/5280=.206

.206 x cadence= mph.


shorter formula is this:

Gear inches times 0.00297 times cadence=speed.

just remember the .00297 and yer good.

I like this one real good... Sheldon Brown's Bicycle Gear Calculator

Nope, the gear inches are the equivalent diameter of a tire if it were using a 1:1 drive (tricycle wheel.) The development is how far you'd travel, which is the gear inches times pi.

Thanks, that's correct. The development needs to use the circumference and not the diameter. I'm going to edit the original post to correct the error.

Welsh, it won't let me quote you...
 

Hope i didn't come across wrong. Long day, and text is a cold medium, anyhow.

I like your 336 number. Ill have to use it more.

easier than .00297

[QUOTE=shorter formula is this:

Gear inches times 0.00297 times cadence=speed.

just remember the .00297 and yer good.[/QUOTE]

The math doesn't work out:
Gear inches x 0.00297 x cadence= speed
(20 inch wheel *42T/20T as stated by [MENTION=313360]welshTerrier2[/MENTION]) x 0.00297 x cadence= 15 mph (as stated by OP)
42 gear inch x 0.00297 x cadence = 15 mph
cadence= 15/42/0.00297
cadence= 120
cadence is quite high

Sometimes I feel like an analog man who's been trapped in a digital universe. I think that you're working at this too hard.

1. Forget about speed for a minute. If you put a Ferrari transmission into some econo box car, it still won't go 150 MPH. You have to have the power to push it.
2. As you ride, when you feel like your feet are spinning too fast, shift into the next hardest gear. If that gear feels too hard, you need a cassette with closer gear spacing.