Physics (kind of) question

Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds
on a bicycle . . .

I recently completed a solo century averaging just over 20mph, and
then this moring I was doing 3-minute intervals and not able to keep
my speed above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25
than at, say, 15? Is it tougher to increase from 25-26 than it is to
increase from 15-16?

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward.
And that a faster body would have more work to do, because the size of
the envelope of compressed air would increase . . .

Does that make any sense? Is there any non-linearity in the
difficulty/speed ratio?

Obviously not a physicist -

Peter

On Aug 6, 10:50*am, b9rel8tor wrote:
Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds
on a bicycle . . .

I recently completed a solo century averaging just over 20mph, and
then this moring I was doing 3-minute intervals and not able to keep
my speed above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25
than at, say, 15? *Is it tougher to increase from 25-26 than it is to
increase from 15-16?

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward.
And that a faster body would have more work to do, because the size of
the envelope of compressed air would increase . . .

Does that make any sense? *Is there any non-linearity in the
difficulty/speed ratio?

Obviously not a physicist -

Peter

Absolutely. I'm more familiar with looking at questions like this in
an automotive context, but roughly speaking, aerodynamic drag
increases with the square of speed. So the faster you're going, the
harder it will be to increase your speed by, say, 1 MPH.

There may be other factors in play such as the rolling resistance of
the tire against the road, but I suspect that aerodynamic drag
accounts for most of what you're observing.

nate

On 2009-08-06, b9rel8tor wrote:
Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds
on a bicycle . . .

I recently completed a solo century averaging just over 20mph, and
then this moring I was doing 3-minute intervals and not able to keep
my speed above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25
than at, say, 15? Is it tougher to increase from 25-26 than it is to
increase from 15-16?

Yes.

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward.
And that a faster body would have more work to do, because the size of
the envelope of compressed air would increase . . .

Something like that. As N8N said, the force applied by the air goes up
roughly as the square of your speed. That means the resistive _power_
goes up as the cube of your speed.

So yes, as you go faster it gets much harder.

These calculators are fun:

http://bikecalculator.com/veloMetricNum.html

Using a similar one, if you do a metric century at 20mph, that's about
205W (which is good going). But to do it at 25mph, you'd need about
365W, which to keep up over 100km is out of the reach of most non-pros.

As you say it's quite hard to keep that pace up even for a few minutes.

Cadel Evans was writting on his "twitter" that just to warm down after
the TdF they do about 150km/200km a day at an average of 40kph.

On Thu, 06 Aug 2009 07:50:46 -0700, b9rel8tor wrote:

Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds on
a bicycle . . .

I recently completed a solo century averaging just over 20mph, and then
this moring I was doing 3-minute intervals and not able to keep my speed
above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25 than
at, say, 15? Is it tougher to increase from 25-26 than it is to
increase from 15-16?

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward. And
that a faster body would have more work to do, because the size of the
envelope of compressed air would increase . . .

Does that make any sense? Is there any non-linearity in the
difficulty/speed ratio?

Obviously not a physicist -

Peter

The simple relation is that air resistance force is proportional to the
square of the relative velocity between the rider and the air. Most
studies relate endurance to power, which is force times velocity. So, the
power is proportional to the cube of the relative velocity. Now, if your
interval was going into a wind and your century had a tailwind...

That holds so long as you are maintaining a constant velocity. There's a
big penalty for trying to accelerate. The force that's required is the
mass of the (rider + bike) times the acceleration. That force usually
comes to a lot more than wind resistance. So, you gave your system a big
jolt, if you tried to accelerate really fast for your interval.

Stephen Bauman

Thanks for the helpful replies!

(It was 100-mile century . . . 50 out/50 back . . . I guess a solo 4-
hour century is out of the question . . . 365 watts for 4 hours! LOL)

On Aug 6, 3:50*pm, b9rel8tor wrote:
Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds
on a bicycle . . .

I recently completed a solo century averaging just over 20mph, and
then this moring I was doing 3-minute intervals and not able to keep
my speed above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25
than at, say, 15? *Is it tougher to increase from 25-26 than it is to
increase from 15-16?

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward.
And that a faster body would have more work to do, because the size of
the envelope of compressed air would increase . . .

Does that make any sense? *Is there any non-linearity in the
difficulty/speed ratio?

Obviously not a physicist -

Peter

Sure, any question with an answer in cubes is a question in physics.
The resistance of the air goes up as the square of velocity, the power
required to maintain that speed increases as the cube... So you got it
right first time: it is proportionately much harder to go from 25mph
to 26mph than it was to go from 24mph to 25mph.

So much for steady speed.

Acceleration adds another energy demand related to your mass and that
of the bicycle (lightweight bikes are really about accelerating from
any speed in highly competitive sports, not about touring or even
commuting). This temporary power demand of acceleration is higher than
merely maintaining a steady speed.

The problem with your intervals is probably to do with an attempt to
accelerate very quickly to the desired speed wiping you. You have to
accelerate slower and more steadily (locally in Ireland we say, "take
it handy"), or choose a lower terminal speed to hold for your
interval.

Andre Jute
Visit Andre's books at
http://www.audio-talk.co.uk/fiultra/THE%20WRITER'S%20HOUSE.html

On 2009-08-06, Still Just Me - wrote:
On Thu, 06 Aug 2009 10:30:24 -0500, Ben C wrote:


Something like that. As N8N said, the force applied by the air goes up
roughly as the square of your speed. That means the resistive _power_
goes up as the cube of your speed.

Does this apply to maintaining that speed as well as getting to that
speed?

To maintaining it. I'm still grappling with Stephen Bauman's suggestion
that acceleration makes much difference-- usually it's very easy to get
up to speed on a bike.

But I haven't done the math. Need to make a graph of ratio of power
going into acceleration vs resistance against actual acceleration in m/s
at a range of speeds.

On Aug 6, 9:30*am, Ben C wrote:
Using a similar one, if you do a metric century at 20mph, that's about
205W (which is good going). But to do it at 25mph, you'd need about
365W, which to keep up over 100km is out of the reach of most non-pros.

Pros can't avg 365W for a long distance either. Using specs for my 170
lb self and riding on the drops, and using the english version of that
calculator http://bikecalculator.com/veloUS.html, I get 176W at 20
mph, and 314W at 25 mph. Which seems about right. The pros manage
higher speeds by drafting and sharing the load, which can work for a
century ride also.

With aerobars they claim only 255W needed to go 25 mph, which IME
would be indicative of a full-on TT kit.

On 6 Aug, 15:50, b9rel8tor wrote:
Greetings from (surprisingly cool) St. Louis!

I have a question about the relative difficulty at increasing speeds
on a bicycle . . .

I recently completed a solo century averaging just over 20mph, and
then this moring I was doing 3-minute intervals and not able to keep
my speed above 25mph for the entire interval.

I was wondering - is the ratio of difficulty to speed "worse" at 25
than at, say, 15? *Is it tougher to increase from 25-26 than it is to
increase from 15-16?

I got to thinking that a moving body (like a biker and his bike) must
push through air, compressing the air in front as it moves forward.
And that a faster body would have more work to do, because the size of
the envelope of compressed air would increase . . .

Does that make any sense? *Is there any non-linearity in the
difficulty/speed ratio?

yes. Eventually you get to a pace where your muscles cannot deliver
any more speed no matter how much harder you try, , , unless of course
you are not trying hard enough. Hard enough for a time trial is when
you are the fastest or blood comes out of your eye sockets. It's
probably best to go a little less than this. 99.99% go less.

On 6 Aug, 18:09, rruff wrote:
On Aug 6, 9:30*am, Ben C wrote:

Using a similar one, if you do a metric century at 20mph, that's about
205W (which is good going). But to do it at 25mph, you'd need about
365W, which to keep up over 100km is out of the reach of most non-pros.

Pros can't avg 365W for a long distance either. Using specs for my 170
lb self and riding on the drops, and using the english version of that
calculatorhttp://bikecalculator.com/veloUS.html, I get 176W at 20
mph, and 314W at 25 mph. Which seems about right. The pros manage
higher speeds by drafting and sharing the load, which can work for a
century ride also.

With aerobars they claim only 255W needed to go 25 mph, which IME
would be indicative of a full-on TT kit.

iirc 170w is what the normally healthy but sedentary person can output
continuously although this does not seem to apply to an untrained
cyclist. The skill of cycling can be learned in 4-6 weeks and this
20mph (3h or more)is usually judged the time for when the cyclist has
flowered. 25mph is considered a good fast regular pace and a faster
pace is for shorter duration. 30mph is high speed for a steady pace
and most can only top this by reaching into their anaerobic reserves.