Rolling resistance - real numbers?

Dave Salovesh said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In other
words, the point being made at that Web site is basically nonsensical.

If you want real numbers, look at rolling resistance tables that convert the coefficient of rolling
resistance to watts of energy absorbed. From the rider's perspective, that's what counts.

Tim McNamara said:

Dave Salovesh said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In
other words, the point being made at that Web site is basically nonsensical.

Well it means that at very low speeds where wind resistance isn't an issue, the 0.4% grade will be
twice as hard to push as level ground. This could be verified experimentally:

Pedal up to a steady and well-measured but very slow speed (to defeat wind resistance, this should
also be done on a windless day) along a surface that's known to be level. Stop pedalling, and
measure the distance you coast before coming to a complete stop.

Now calculate the height your bicycle could have climbed with your original kinetic energy h =
v^2/2g where v was your original speed and g acceleration due to gravity. Divide h by the distance
you coasted and the ratio will give you an equivalent grade that you could climb on a lossless bike
with the same effort.

This experiment takes into account ALL the losses of the bike, not just rolling resistance, which
may make it more, or less useful depending on your perspective.

Dave Salovesh <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Tom Compton (through the "Forces on Rider" calculator at Analytic Cycling,
analyticcycling.comForcesSource Page.htmlOpen ↗) seems to make the assumption that rolling
resistance on asphalt contributes as much to drag as would climbing a grade of 0.4%, e.g., 1 ft.
over ~4.75 mi., i.e., really really little.

This factor is used in the calculator to compare riding surfaces, and other examples suggest a
factor of 0.1% for a wooden track, 0.2% for smooth concrete, and 0.8% for a rough but paved road.

I don't disagree (much) with the relative positions of the road surfaces, but I'm curious if
anyone knows of data that could clarify the absolute comparison to grade a bit.

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Dear Dave,

I don't know how the details were worked out, but at least the scale seems to run upward for
increasingly rough surfaces, so it's plausible. Obviously, there's a fair range from smooth 0.4%
"asphalt" up to needs-paving .8% "rough but paved."

Grade-percentages are tricky, from what I've seen in the archives here, but a 0.4% grade may be
steeper than your one foot in 4.75 miles. If a 4% grade means a 4-foot rise in a 100-foot run, then
a 0.4% grade means a 4-foot rise in a 1,000-foot run.

A thread last year with exciting details can be found here:

groups.google.comgroupsOpen ↗
8&selm=3CCDA4A9.8020706%40nospam.attbi.com

Since the percentages start diverging around 20%, it's possible that they get weird under 1%. If
we're lucky, Mark Janeba will scribble some figures on the back of an envelope.

With my crude 6-foot thick-wall white-pipe grade-checker whose slit lets me drop the ruler of a
carpenter's level at 50 inches, a 0.4% grade would show up as a drop of just a hair over 3/16ths of
an inch in 50 inches, less than the expected irregularities that accumulate in about four feet of
middle-aged pavement.

Table 5.2 on page 117 of "Bicycling Science" lists these coefficients of friction for ancient
surfaces from various sources:

.004 _ _ _ racing track .005-0.010 road .013-0.016 smooth macadam road .015 _ _ _ flag pavement .014-
0.017 flint (again) .016 _ _ _ macadam road .023 _ _ _ broken granite

There may be a similar table in Archibald Sharp's much earlier "Bicycles and Tricycles," but I'm
still negotiating with Santa for a copy.

Of course, the easiest thing to do would be to email Tom Compton at his site and ask him how he did
it, but what fun would that be?

"Well, three or four months run along, and it was well into the winter now. I had been to school
most all the time and could spell and read and write just a little, and could say the multiplication
table up to six times seven is thirty-five, and I don't reckon I could ever get any further than
that if I was to live forever. I don't take no stock in mathematics, anyway."

--Huckleberry Finn

Carl Fogel

Tim McNamara said:

Dave Salovesh said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In
other words, the point being made at that Web site is basically nonsensical.

Well, that's what was meant, I'm sure. It's hypothetical, but it's not nonsensical. It gives a
person a feel for how much (or how little) improvement is possible regarding rolling
resistance. IOW, if you had "perfect" tires, with no rolling resistance, it wouldn't make you
ride like Superman.

Quoted message said:

If you want real numbers, look at rolling resistance tables that convert the coefficient of
rolling resistance to watts of energy absorbed. From the rider's perspective, that's what counts.

See terrymorse.comrolres.htmlOpen ↗ and see the link to discussion by somebody
named Jobst.

Looks to me like at 7 kgf/cm^2 (= 100 psi) a median value might be 250 g force resistance. The
tests were with a 50 kg load, so that's 0.5% - but it was on a steel drum. I didn't see the
diameter quoted.

Smooth steel would be better than the road, but a curved drum would be worse, I'd guess.

--
Frank Krygowski [To reply, omit what's between "at" and "cc"]

Tim McNamara <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

Quoted message said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In
other words, the point being made at that Web site is basically nonsensical.

I don't see why it is nonsensical. The point is surely that rolling resistance is eqivalent to 0.4%
of your weight.

It thus factors into calculations the same as a 0.4% gradient.

Andrew Bradley

In <[email hidden]>,
Tim McNamara <[email hidden]> opined:

Quoted message said:

Dave Salovesh said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In
other words, the point being made at that Web site is basically nonsensical.

I put it too briefly:

Given two tires on the same level surface where one tire has a 0.004 Crr and the other has 0.008 -
does the 0.008 Crr give the same effective drag as taking the 0.004 Crr tire up a 0.4% grade?

Quoted message said:

If you want real numbers, look at rolling resistance tables that convert the coefficient of
rolling resistance to watts of energy absorbed. From the rider's perspective, that's what counts.

Here's a nice table like that:

users.globalnet.co.uklafford.htmOpen ↗

Looks about like a change of 0.0001 in Crr costs somewhere between 1 and 2 watts when we're dealing
with typical bicycle ranges.

But that quantitative info only helps if you have accurate ways to measure output in watts and a
good sense of fine differences in them in the practical world.

For everyday people I want to come up with a more qualitative and subjective way to express the
watts absorbed by varying the Crr.

I like what I see in the calculator in that I can equate a change in Crr to a change in grade -- but
I'm dubious that the decimal grade is an exactly equal factor to the Crr...

--
[email hidden] | depending, of course, | REPLACE example WITH Dave Salovesh | on your
perspective | mindspring TO EMAIL ME (After more than a decade on USENET , it's finally come
to this ^^^)

In <[email hidden]>,
[email hidden] (Carl Fogel) opined:

Quoted message said:

Grade-percentages are tricky, from what I've seen in the archives here, but a 0.4% grade may be
steeper than your one foot in 4.75 miles. If a 4% grade means a 4-foot rise in a 100-foot run,
then a 0.4% grade means a 4-foot rise in a 1,000-foot run.

Oops - somewhere in my number play I lost track of the difference between decimal grade (used in the
cited calculator) and percentage (used by mortals), and I effectively figured the rise over run/100.
So yes, a 0.4% grade changes 1 foot in 250, not in 25,000.

Still not a major slope, but it does help me understand the feel a bit better. My original numbers
sure didn't seem right -- shoulda known...

(snip)

Quoted message said:

Table 5.2 on page 117 of "Bicycling Science" lists these coefficients of friction for ancient
surfaces from various sources:

.004 _ _ _ racing track .005-0.010 road .013-0.016 smooth macadam road .015 _ _ _ flag pavement
.014-0.017 flint (again) .016 _ _ _ macadam road .023 _ _ _ broken granite

Thanks - those numbers appear a bit higher than suggested in the calculator.

(snip)

Quoted message said:

Of course, the easiest thing to do would be to email Tom Compton at his site and ask him how he
did it, but what fun would that be?

I simply noticed that when I play with numbers in that calculator, if I take the suggested Crr
number for a given surface and plug it exactly as shown into the "Grade of hill" field (which
expects a decimal value, not a percent one), the calc says the effective drag from climbing is the
same as from rolling resistance.

I can understand that just fine, but I'm not sure the equivalence is accurate.

(In fact, the site apparently provides the equation used (as a glossary example of a differential
equation) but it's one of those things like Visual Basic where I can easily understand the general
flow but the details make my head spin.)

"Math is HARD. Let's go shopping."

--Barbie

--
[email hidden] | depending, of course, | REPLACE example WITH Dave Salovesh | on your
perspective | mindspring TO EMAIL ME (After more than a decade on USENET , it's finally come
to this ^^^)

I have book by Witt and Wilson which includes a table of Crr values for several different tires and
surfaces. If I recall correctly, a Conti Olympic was the best at .16% and some silk tires were about
.22% Other tires ranged up to .6%. Of course surface has an effect as well.

"Andrew Bradley" <[email hidden]> wrote in message
"]news:[email hidden]...

Quoted message said:

Tim McNamara <[email hidden]> wrote in message

news:<[email hidden]>...

Quoted message said:

Quoted message said:

Quoted message said:

Is riding on level asphalt really equivalent to climbing a 0.4% grade?

Only compared to climbing that 0.4% hill on a surface that afforded no rolling resistance. In
other words, the point being made at that Web site is basically nonsensical.

I don't see why it is nonsensical. The point is surely that rolling resistance is eqivalent to
0.4% of your weight.

It thus factors into calculations the same as a 0.4% gradient.

Andrew Bradley

Dave Salovesh said:

I like what I see in the calculator in that I can equate a change in Crr to a change in grade --
but I'm dubious that the decimal grade is an exactly equal factor to the Crr...

Well, it is. It's _much_ easier to explain if you've had a couple physics courses, though.

Try getting a good physics text or engineering mechanics text, and reading the part about "angle of
friction" or perhaps "angle of repose." They'll probably cover this issue, or come very close to it.
You'll need to keep in mind that the Crr is just another version of the coefficient of friction.

--
Frank Krygowski [To reply, omit what's between "at" and "cc"]

In <[email hidden]>,
"frkrygow" <"frkrygow"@omitcc.ysu.edu> opined:

Quoted message said:

Dave Salovesh said:

I like what I see in the calculator in that I can equate a change in Crr to a change in grade --
but I'm dubious that the decimal grade is an exactly equal factor to the Crr...

Well, it is. It's _much_ easier to explain if you've had a couple physics courses, though.

But I don't -ride- physics! ;-)

I asked google to tell me about: watts climb hill. Third return,
etape.org.ukMaths.htmOpen ↗ said:

Power (Watts) = 2 x Weight(lb) x Speed(mph) x Gradient (as a fraction)

(for the sticklers, a footnote on that page explains why this is both wrong and close enough.)

Using data for the Vredestein Fortezza Piste from yesterday's find at
users.globalnet.co.uklafford.htmOpen ↗ (Crr=0.0043, mph=30, weight=200) and using Crr
in place of gradient in then equation gives me:

2 x 200 x 30 x 0.0043 = 51.6

Which lines up very well with the 52 watts listed in the Lafford report. My skeptical nature still
wonders if the report actually measured watts absorbed or simply calculated them the way I just did,
but as the report is widely cited as a good collection of tire performance data I'll mostly accept
it as given. Mostly...

So said:

Well, it is.

--
[email hidden] | depending, of course, | REPLACE example WITH Dave Salovesh | on your
perspective | mindspring TO EMAIL ME (After more than a decade on USENET , it's finally come
to this ^^^)

Dave Salovesh <[email hidden]> wrote in message news:<[email hidden]>...

Quoted message said:

In <[email hidden]>, Tim McNamara <[email hidden]> opined:

I put it too briefly:

Given two tires on the same level surface where one tire has a 0.004 Crr and the other has 0.008 -
does the 0.008 Crr give the same effective drag as taking the 0.004 Crr tire up a 0.4% grade?

In a word YES. Here's my numbers for a standard cyclist riding in an MTB position (on the tops) for
hill slope 0.4% and Crr 0.004.

*** "Rik's Analysis" ***

Input Parameters
----------------
Cyclist Velocity [mile/h] .............. 18.000 Hill Slope [degree] .................... 0.40
Cyclist Mass [lb] ...................... 168.00 Cyclist Height [inch] .................. 70.00
Cyclist Gender ......................... Male Cw (Coefficient of Drag) ............... 0.90 Wheel
Diameter [inch] .................. 26.00 Wheel Circumference [inch] ............. 53.39 Bicycle Mass
[lb] ...................... 25.50 Air Density [kg/m^3] ................... 1.225 Rolling Resistance
Coefficient ......... 0.0040 Bicycle Transmission Efficiency ........ 0.970 Cadence (RPM)
.......................... 90 Chainring Size ......................... 36

Derived Parameters
------------------
Vector Velocity [km/h] ................. 28.962 Vector Velocity [m/s] .................. 8.045 Gear
Development [m] ................... 5.363 Gear Size [inch] ....................... 67.21 Gear Ratio
............................. 36X13.93 Cyclist Body Surface Area [m^2] ........ 1.938 Cyclist
Frontal Area [m^2)] ............ 0.3489 Cw_FA [m^2] ............................ 0.3140

Results
-------
Power Total [W] ........................ 161.0 Power Air Resistance [W] ............... 100.1 62.22%
Power Rolling Resistance [W] ........... 28.0 17.39% Power Drive Train [W] .................. 4.8
3.00% Power Hill [W] ......................... 28.0 17.39%

Power Total [hp] ....................... 0.216

Here's my numbers for hill slope 0.0% and Crr 0.008

Results
-------
Power Total [W] ........................ 161.0 Power Air Resistance [W] ............... 100.1
62.22% Power Rolling Resistance [W] ........... 56.0 34.78% Power Drive Train [W]
.................. 4.8 3.00%

Power Total [hp] ....................... 0.216

You should note that a Crr value of 0.004 would be difficult to achieve on a normal road even with
good clincher/tubulars - the road would have to be very smooth asphalt (equivalent to a concrete
surfaced velodrome).

-Rik