Math question (Trainer)

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

Quick and dirty approximate answer:
(Chainring size/cog size)*(pedal cadence (in rpm))*.08
gives speed in mph.

For your numbers, 53/14*100*.08 ~= 30mph.

Mark

"Hell and High Water" wrote: If I was doing this on the road, how fast would
I be travelling? (clip)
^^^^^^^^^^^^^^^
The resistance setting doesn't matter. I get pretty close to 30 MPH.
However, called the wheel diameter 27"--don't know the correct diameter of a
700 wheel.

Multiply pedal RPM by chain ring teeth, and divide by cog teeth. That gives
you wheel RPM. Then calculate circumference of wheel (pi x diameter) and
multiply to get distance per minute. If diameter was given in inches, then
you will get speed in inches per minute. So divide by 12 and by 5280 to get
miles per minute. x 60 gives miles/hour.

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.
Front chainring is 53
Rear cog is 14
Tires are 700 x 23
If I was doing this on the road, how fast would I be travelling?
THANKS!

-Bob

You would be going 26.66 mph

Using this calculator recalculate for MPH at Bottom after fist
calculation> http://www.panix.com/~jbarrm/cycal/cycal.30f.html

Based on your wheel size being 668mm in diameter. Based on ISO formula
at bottom of Sheldon's page.
http://sheldonbrown.com/cyclecomputer-calibration.html

John

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.
Front chainring is 53
Rear cog is 14
Tires are 700 x 23 > Trainer is set to the middle of three resistance settings
If I was doing this on the road, how fast would I be travelling?

Quoted message said:

-Bob

You would be going 29.62MPH at 100 rpms

See here> http://www.panix.com/~jbarrm/cycal/cycal.30f.html

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

Without some objective gauge of the resistance ofthe trainer, it's
impossible to say. If you used a powermeter on your bike while on the
trainer to get a reading, then went outside and rode the same rpm and
same power output (likely with a different gear) you could approximate
the speed.

JT

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"Hell and High Water" <[email hidden]> wrote in message
news:[email hidden]...

Quoted message said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

(seriously....this isn't a trick question. I just don't know how to
figure it out...)

(82.5/12)*(53/14)*(100/60)*(60/88) = 29.57 mph.

Rolling circumference of 70x23 tire = 82.5 inches
53/14 = gear ratio
100/60 = rev/sec
60/88 converts ft/sec to mph.

Phil H

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

It's impossible to make even an educated guess with the information.
Most of the answers so far, I believe, missed the point. Your rear tyre
is spinning at 29.6 mph, but to estimate how fast you would be going on
the road with the same level of EFFORT we need to know what your
POWER output is.

Assuming that you're trainer doesn't have a display showing wattage,
it's difficult to tell. Have you checked if your trainer's manual has a
graph showing the wattage given speed with the three resistance
settings?

-as

In article <[email hidden]>,
[email hidden] says...

Quoted message said:

It's impossible to make even an educated guess with the information.
Most of the answers so far, I believe, missed the point. Your rear tyre
is spinning at 29.6 mph, but to estimate how fast you would be going on
the road with the same level of EFFORT we need to know what your
POWER output is.

Effort has nothing to do with it.

If I'm in a measurable gear, pedaling at a measurable rate, I'll be
travelling at a measurable speed.

It's mathematics.

Now...If I'm out on the road, there's a lot more to being able to pedal
at that cadence in that gear, but if I DID IT, I'd be travelling at a
certain speed.

-Bob

In article <[email hidden]>, piholmanz@yourservice
says...

Quoted message said:

(82.5/12)*(53/14)*(100/60)*(60/88) = 29.57 mph.

Rolling circumference of 70x23 tire = 82.5 inches
53/14 = gear ratio
100/60 = rev/sec
60/88 converts ft/sec to mph.

This one looks right to me.

700 x 23 is 82.5 inches?

If that's correct, this makes sense.

THANKS!

-Bob

Hell and High Water said:

If I'm in a measurable gear, pedaling at a measurable rate, I'll be
travelling at a measurable speed.

It's mathematics.

Nice troll.

JT

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Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

(seriously....this isn't a trick question. I just don't know how to
figure it out...)

THANKS!

-Bob

Some great answers have been given here, but it depends on which
is the dominant factor - your cadence or the power you're putting
out. If the cadence dominates, the power will fluctuate with
grade and wind resistance, etc, and most of the math here is
correct. If the power is kept constant, the cadence and speed
will be a function of grade and wind.

p.

In article <[email hidden]>,
[email hidden] says...

Quoted message said:

Hell and High Water said:

If I'm in a measurable gear, pedaling at a measurable rate, I'll be
travelling at a measurable speed.

It's mathematics.

Nice troll.

??

Not sure I get that one...

-Bob

Hell and High Water said:

I'm on my trainer and I'm pedaling exactly 100 RPM.

Front chainring is 53

Rear cog is 14

Tires are 700 x 23

Trainer is set to the middle of three resistance settings

If I was doing this on the road, how fast would I be travelling?

Well, if you mean how fast you'd be going with that rpm:

(53/14 * 100 Rotations Per Minute * 60 Minutes/hour *
((622 + 2 * 23 millimeters rim diameter)* pi) /10^6= kilometers per hour.
Google for (53/14 * 100 * 60 * ((622 + 2 * 23) * pi )/10^6 (removing the
units google calc doesn't understand) and it tells you the answer is
47.67.

On the other hand, the middle of three resistance settings almost
certainly provides much less resistance than rolling resistance and wind
resistance would out on the road, so your actual power output, measured
against the actual road, would probably be quite a bit slower.

Jasper

In article <[email hidden]>, [email hidden]
says...

Quoted message said:

Some great answers have been given here, but it depends on which
is the dominant factor - your cadence or the power you're putting
out. If the cadence dominates, the power will fluctuate with
grade and wind resistance, etc, and most of the math here is
correct.

Exactly.

I was specific in that I was pedaling at exactly 100 rpm.

If I was in the exact same gear, pedaling the exact same rpm, I'd be
traveling at a given, measurable speed. Regardless of how hard or soft
I was pushing on the pedals.

The gearing is set. One pedal revolution equates to (x)tire revolution.
There would not be any 'slippage.'

(82.5/12)*(53/14)*(100/60)*(60/88) = 29.57 mph.

Rolling circumference of 70x23 tire = 82.5 inches
53/14 = gear ratio
100/60 = rev/sec
60/88 converts ft/sec to mph.

(I believe that answer is correct.)

-Bob

Hell and High Water said:

Effort has nothing to do with it.

If I'm in a measurable gear, pedaling at a measurable rate, I'll be
travelling at a measurable speed.

It's mathematics.

Now...If I'm out on the road, there's a lot more to being able to pedal
at that cadence in that gear, but if I DID IT, I'd be travelling at a
certain speed.

-Bob

There are a number of programs that can calculate the info you
supplied and do much more. One I really like is GearCalc, here take a
look: http://www.income-software.com/index.htm?GearCalc/gc_index.asp

It is real helpful for planning a drivetrain, it includes gear ratios,
gear inches, cadence info, and much more.

Life is Good!
Jeff

Jasper Janssen said:

tells you the answer is 47.67.

That's 47.67 km/hour. Or about 29.8 mph.

The easy to remember formula is:

Gear Ratio * Wheel Diameter (inches) * Cadence (rpm) * 0.00297 = MPH

53/14 * 26.5 inches * 100 * 0.00297 = 29.8 mph

The 0.00297 is the fudge factor that brings all the units into line.

Art Harris

In article <[email hidden]>,
[email hidden] says...

Quoted message said:

Jasper Janssen said:

tells you the answer is 47.67.

That's 47.67 km/hour. Or about 29.8 mph.

The easy to remember formula is:

Gear Ratio * Wheel Diameter (inches) * Cadence (rpm) * 0.00297 = MPH

53/14 * 26.5 inches * 100 * 0.00297 = 29.8 mph

The 0.00297 is the fudge factor that brings all the units into line.

On a side note, I went out for a ride this morning, dropped it into that
exact gear, 53x14, pedaled with the same tune in my head, Stones 'Beast
of Burden', looked down at the speedo and it was showing 29.

SCIENCE!!

;-)

-Bob

If I was doing this on the road, how fast would I be travelling?
^^^^^^^^^^^^^^^
It's impossible to make even an educated guess with the information. (clip)
^^^^^^^^^^^^^^^
I can do better than an educated guess--I can give you an EXACT ANSWER. You
would not be moving at all. The trainer stays put, no matter how fast you
pedal or where it is located. ;-)

"Hell and High Water" wrote: (clip) looked down at the speedo and it was
showing 29.

Quoted message said:

SCIENCE!!

^^^^^^^^^^^^^^^^^^^^
I think you should enter those results in a science fair. Can you help me
design an experiment that verifies that 2 + 2 = 4? <G>