Rollers math fun?

[Ron Ruff]

Doh! I goofed...

Spreading the load on the rear wheel over two rollers doesn't help at
all... for some reason I was thinking it would cut it in half.

While I'm at it I guess I'll calculate the effect of roller spacing
too. If the rollers are 10 inches apart then the increased pressure on
the wheel would be:

(27^2+10^2)^.5/27= 1.07... not very much. Since more of the weight is
on the rear wheel I'll say the overall increase is a factor of 1.04
which is too small to worry about.

So... from my earlier post, the rolling resistance is 5 times higher
with 3 inch rollers. So:

P=Crr_road*5*Mg*V

for V in km/hr and M in kg

P=13.6*Crr_road*M*V

If we slap in a Crr of .006, M=85kg, and V=40km/hr, we get

P= 277W

If you throw in 10W for aero resistance, then divide by .95 to account
for transmission efficiency, you have P= 302W... which coincidentally
is what the graph here shows for the 3 inch rollers:
http://www.geocities.com/almost_fast/trainerpower/

If you happen to have a power meter, then this should be a decent way
to determine the rolling resistance of the tires.

 

[[email protected]]

Ron Ruff wrote:
> Dan Connelly wrote:
> >
> > Suppose, for sake of argument, the wheel resistance is reduced by 2/3 when translational
> > resistance is eliminated (this obviously depends on spoke count, spoke shape, rim profile,
> > etc). Then wheel resistance is only 8 to 13 watts. Rolling resistance remains 34 watts.
> >
> When a wheel is being ridden, the power needed to spin it is much
> higher, because some of the spokes are seeing a wind that is double
> forward velocity... which results in a factor of 8 in power on these
> spokes. Of course some are seeing essentially zero wind as well.
> Eliminating both the translational drag and the extra power to spin on
> the road would likely drop the drag even more than 2/3.
>
> On rollers the rolling resistance goes up a lot, as I showed earlier.
> Using your values for weight and speed, with a Crr of .024, the power
> would be:

> .024*780N*11m/s= 206W

My rollers are 4.5" which should be about 3.9x "normal" RR, or about
..023. Not much difference there. Me and the bike exert 105kgf or
1030N.

0.023*1030*11m/s = 260W + 10W to spin the wheels (or 10 + 10?) = 270W.

Sounds about right for my level of exertion at that speed. And my
presumed max power calculated based on climbs is about 310W which also
matches my more or less max of <45km/h on the rollers.

Pretty cool!

Joseph

 

[[email protected]]

Ron Ruff wrote:
> Dan Connelly wrote:
> >
> > Suppose, for sake of argument, the wheel resistance is reduced by 2/3 when translational
> > resistance is eliminated (this obviously depends on spoke count, spoke shape, rim profile,
> > etc). Then wheel resistance is only 8 to 13 watts. Rolling resistance remains 34 watts.
> >
> When a wheel is being ridden, the power needed to spin it is much
> higher, because some of the spokes are seeing a wind that is double
> forward velocity... which results in a factor of 8 in power on these
> spokes. Of course some are seeing essentially zero wind as well.
> Eliminating both the translational drag and the extra power to spin on
> the road would likely drop the drag even more than 2/3.
>
> On rollers the rolling resistance goes up a lot, as I showed earlier.
> Using your values for weight and speed, with a Crr of .024, the power
> would be:

> .024*780N*11m/s= 206W

My rollers are 4.5" which should be about 3.9x "normal" RR, or about
..023. Not much difference there. Me and the bike exert 105kgf or
1030N.

0.023*1030*11m/s = 260W + 10W to spin the wheels (or 10 + 10?) = 270W.

Sounds about right for my level of exertion at that speed. And my
presumed max power calculated based on climbs is about 310W which also
matches my more or less max of <45km/h on the rollers.

Pretty cool!

Joseph

 

[Ron Ruff]

Kinky Cowboy wrote:
>
> 0.023*980N*24m/s = 540W sprinting
> 0.023*980N*14.7m/s = 330W time trialling
>
> This is quite a big difference from the estimated 260W for riding on
> the road at the same intensity.

The resistance on the rollers is highly dependant on the rolling
resistance of your tires. The .023 number you are using is based on a
flat-road Crr of .006... and this should be a decent estimate for an
average road tire. If you are using very good racing tires the Crr
might be .004 (.0156 instead of .023 in the above equation), which
would be only 2/3 the resistance on the rollers... instead of 330W at
14.7m/s you'd be at 220W.

Since the tire rolling resistance is not a precisely known or even
stable quantity (it varies with temperture, wear, and inflation...
maybe age?, and certainly by tire model), it isn't possible to use it
to determine your power accurately...

.... which is why I didn't think this would be a very *useful*
exercise...

.... but maybe Joseph is having fun...

 

[[email protected]]

Ron Ruff wrote:

> ... which is why I didn't think this would be a very *useful*
> exercise...
>
> ... but maybe Joseph is having fun...

Fun and utility are infrequently linked in my world ;-)

Joseph

 

[[email protected]]

Ron Ruff wrote:
> Kinky Cowboy wrote:
> >
> > 0.023*980N*24m/s = 540W sprinting
> > 0.023*980N*14.7m/s = 330W time trialling
> >
> > This is quite a big difference from the estimated 260W for riding on
> > the road at the same intensity.
>
> The resistance on the rollers is highly dependant on the rolling
> resistance of your tires. The .023 number you are using is based on a
> flat-road Crr of .006... and this should be a decent estimate for an
> average road tire. If you are using very good racing tires the Crr
> might be .004 (.0156 instead of .023 in the above equation), which
> would be only 2/3 the resistance on the rollers... instead of 330W at
> 14.7m/s you'd be at 220W.

Do you suppose rollers would be a good way to measure RR of various
tires based on effort? Since RR is so pronounced at 1030N small changes
would be easier to detect, right? Since I don't have a power meter I'd
have to use HR as a secondary indicator.

So the question becomes, would RR as measured on rollers, be reasonably
directly applicable to RR on the road?

One of my next projects is to determine the most optimal tires for my
needs, and RR is a major concern.

Joseph

 

[Dave Larrington]

In article <[email protected]>,
([email protected]) wrote:

> Do you suppose rollers would be a good way to measure RR of various
> tires based on effort? Since RR is so pronounced at 1030N small changes
> would be easier to detect, right? Since I don't have a power meter I'd
> have to use HR as a secondary indicator.
>
> So the question becomes, would RR as measured on rollers, be reasonably
> directly applicable to RR on the road?
>
> One of my next projects is to determine the most optimal tires for my
> needs, and RR is a major concern.

Some say not, but Ian Sims noted that the differences in rolling
resistance he found testing tyres with a small-diameter roller /were/
mirrored in velodrome tests.

--
Dave Larrington - <http://www.legslarry.beerdrinkers.co.uk/>
My liver is evil, and must be punished.

 

[Jens]

Ron Ruff wrote:
>
> So... from my earlier post, the rolling resistance is 5 times higher
> with 3 inch rollers. So:
>
> P=Crr_road*5*Mg*V
>
> for V in km/hr and M in kg
>
> P=13.6*Crr_road*M*V
>
> If we slap in a Crr of .006, M=85kg, and V=40km/hr, we get
>
> P= 277W
>
> If you throw in 10W for aero resistance, then divide by .95 to account
> for transmission efficiency, you have P= 302W... which coincidentally
> is what the graph here shows for the 3 inch rollers:
> http://www.geocities.com/almost_fast/trainerpower/
>
> If you happen to have a power meter, then this should be a decent way
> to determine the rolling resistance of the tires.

I posted some roller power results with different tires a while ago.
I only have the rear wheel on the rollers - the front is on a stand

Here's a quick sum of the data I got.

Vittoria KS clincher 30.87mph 111.4 watts
Veloflex carbon tubular 30.67mph 133.3 watts
Michelin pro race 30.95mph 121.4 watts

Using the following formula:

power - 15 watts = 10.8 * weight * velocity * crr

I actually stuck a scale under the rear wheel and got
a weight of 46Kg. I subtract the 15 watts for

So I calculate the following Crr figures:

Vittoria: .00388
Veloflex: .00479
Pro Race: .00427

This comes pretty darn close to the Tour magazine figures:

Vittoria: .0039
Veloflex .0049
Pro Race: .0042


The only discrepancy is that the Veloflex does a little better in my
test.
This could be because it was on an aero (404) rim; whereas the others
were on a mid-section rim. The Michelin they tested was a Pro Race II,
which may be better than the Pro Race I tested.


--jens

 

[[email protected]]

Jens wrote:
> So I calculate the following Crr figures:
>
> Vittoria: .00388
> Veloflex: .00479
> Pro Race: .00427
>
> This comes pretty darn close to the Tour magazine figures:
>
> Vittoria: .0039
> Veloflex .0049
> Pro Race: .0042
>
>
> The only discrepancy is that the Veloflex does a little better in my
> test.
> This could be because it was on an aero (404) rim; whereas the others
> were on a mid-section rim. The Michelin they tested was a Pro Race II,
> which may be better than the Pro Race I tested.

That is very interesting. I have subjectively tested a whole bunch of
tires this year, and I have two clear favorites: Pro race II, and
Evo-KS. I haven't previoulsy seen any of this info on comparative Crr
values. My judgement was based solely on feel. I can't say the tires
felt faster, but I do belive they felt more comfortable and sure on
rough surfaces, which I guess would be a result of them being more
supple.

I don't have any Michelin tires mounted now so I can't measure, but I
recall that they are quite a bit wider than the KS for the same nominal
size. Does anyone know for sure if this is the case?

Joseph

 

[[email protected]]

Ron Ruff wrote:
> [email protected] wrote:
> >
> > Do you suppose rollers would be a good way to measure RR of various
> > tires based on effort? Since RR is so pronounced at 1030N small changes
> > would be easier to detect, right? Since I don't have a power meter I'd
> > have to use HR as a secondary indicator.
> >
> Maybe *you* could use HR as an indicator, but mine seems to vary a
> lot... day to day, and from the beginning to the end of a ride. Still,
> it would be better than nothing... and not too bad if you could always
> use a "control" wheel and make comparisons to that, switching back and
> forth a couple of times.
>
> > So the question becomes, would RR as measured on rollers, be reasonably
> > directly applicable to RR on the road?
> >
> As far as I know, yes... with one major caviat. When you are on a
> "non-smooth" surface (which all roads are to some degree), the bike
> will vibrate, and a lot of this energy will get absorbed (wasted). On
> the rollers or a track, you can pump up the tires to 150psi or more and
> they will keep getting better... but on a rougher surface there will be
> an optimum pressure... usually 120psi or less... sometimes a lot less.
>
> As far as the actual tire losses are concerned, I'd expect the ones
> that perform best on the rollers would also perform best on the road...
> but I'm not sure that this is true of the vibration losses. Possibly a
> heavier and stiffer tire running a low pressure would do best on a
> rough road, because less energy would be transfered to the rider's
> body, where most of it would be absorbed.
>
> I'm not even talking about comfort here... this strictly an energy loss
> that directly effects the power available to propel the bike. It goes
> up exponentially with frequency also, so it should mimic aero
> resistance when doing field testing, rather than rolling resistance.

For my purposes, comfort is essential, so I won't ever be running more
than say 110psi on 700x23's. Comfort is defined not just as bump
absorbtion, but also solid feel on rough surfaces. I can't stand the
skittish feeling of cornering on rough pavement with super high
pressures.

Given my imposed constraint of around 110psi, would you say it is safe
to assume that relative Crr's will transfer to rough surfaces? My
110psi may not be optimal at any given time, but do you think that if
it is determined that KS's are better than say Pro II's on rollers,
that they will always be better than Pro II's even in suboptimal
conditions? Did that make sense?

As for rough surface induced vibration losses in the frame (and one's
butt) is that actually a bad thing? Is vibrating and heating up the
frame worse than lifting the bike and rider over a tiny bump? I guess
absorbing it with the tire is best, but why is this the case?

Joseph

 

[Ron Ruff]

[email protected] wrote:
> Given my imposed constraint of around 110psi, would you say it is safe
> to assume that relative Crr's will transfer to rough surfaces? My
> 110psi may not be optimal at any given time, but do you think that if
> it is determined that KS's are better than say Pro II's on rollers,
> that they will always be better than Pro II's even in suboptimal
> conditions? Did that make sense?
>

My guess would be yes... especially if they also "feel" smoother on a
rough road.

I wish there was a way to quantify this... but I suspect that "feel" is
a pretty decent way to determine the optimum pressure for best speed.
If you are getting a noticable level of vibration, then dropping the
pressure would probably enable you to go faster, because the decrease
in vibration losses would more than offset the increase in rolling
resistance. On rough roads, lowering the pressure to where pinch flats
are just avoided is probably the fastest.

> As for rough surface induced vibration losses in the frame (and one's
> butt) is that actually a bad thing?

Energy that gets absorbed in your body is a "loss" like any other
frictional loss in the bike-rider system.

I'm no expert, but I'd expect the tires and the frame to be quite
elastic compared to the body... meaning that they will deform and
spring back with little energy lost through damping. A large hunk of
meat is not very "springy" though...

 

[Ron Ruff]

This is great, Jens! I hope other people with power meters and rollers
will do some testing, so we can get some good rolling resistance data
on tires!

Jens wrote:
>
> power - 15 watts = 10.8 * weight * velocity * crr
>

Where did the 10.8 factor come from? Is it just there to give you Crrs
in the range you would expect, or is it derived somehow?

> I actually stuck a scale under the rear wheel and got
> a weight of 46Kg. I subtract the 15 watts for
>

It looks like the end of that sentence was cut off. You'd want to
subtract for aero and drivetrain losses... 15 watts is probably close.

 

[[email protected]]

Ron Ruff wrote:
> This is great, Jens! I hope other people with power meters and rollers
> will do some testing, so we can get some good rolling resistance data
> on tires!
>
> Jens wrote:
> >
> > power - 15 watts = 10.8 * weight * velocity * crr
> >
>
> Where did the 10.8 factor come from? Is it just there to give you Crrs
> in the range you would expect, or is it derived somehow?
>
> > I actually stuck a scale under the rear wheel and got
> > a weight of 46Kg. I subtract the 15 watts for
> >
>
> It looks like the end of that sentence was cut off. You'd want to
> subtract for aero and drivetrain losses... 15 watts is probably close.

Can you pedal the wheel in the air in a work-stand or something by hand
to figure the aero and drivetrain loss for the back wheel at least?

Joseph

 

[Ron Ruff]

[email protected] wrote:
>
> Can you pedal the wheel in the air in a work-stand or something by hand
> to figure the aero and drivetrain loss for the back wheel at least?
>
You could estimate the aero losses calculating the moment of inertia
and measuring the deceleration rate of the wheel.

I found an article online where they measured this:
http://www.damonrinard.com/wheel/grignon.htm

If I did the calculation right, .050 N-m @ 40km/hr works out to only
1.65W. The non-aero wheels were about double that... but it is a small
amount anyway.

Drivetrain losses aren't so easy. I've seen some test results that
indicate losses of more than 10% when the chain tension is low... and
on rollers this is usually the case, especially if the rollers are
fairly large. I'll check into that in more detail, and maybe summarize
things when I get a chance.

 

[Jens]

[email protected] wrote:
> Ron Ruff wrote:
> > This is great, Jens! I hope other people with power meters and rollers
> > will do some testing, so we can get some good rolling resistance data
> > on tires!
> >
> > Jens wrote:
> > >
> > > power - 15 watts = 10.8 * weight * velocity * crr
> > >
> >
> > Where did the 10.8 factor come from? Is it just there to give you Crrs
> > in the range you would expect, or is it derived somehow?

That's the number that made my tests fit nicely with the
3 known CRR figures. I figure if I can match 3 that close,
the values that I get for other tires should be pretty close.
Unfortunately, there are a few subtleties that can screw
up the calculations. In particular, if you shift the front
wheel stand just a little, so the rear wheel doesn't sit very
precisely half way between the 2 rear rollers, the wattage
figures will change.


> >
> > > I actually stuck a scale under the rear wheel and got
> > > a weight of 46Kg. I subtract the 15 watts for
> > >
> >
> > It looks like the end of that sentence was cut off. You'd want to
> > subtract for aero and drivetrain losses... 15 watts is probably close.

I'm using an SRM, which I have previously tested against a powertap,
with the SRM reading 6-8 watts higher. The other 7-9 watts is for
friction in the roller bearings and the little rubber drive belt, and
air
resistance for spinning the wheel.

>
> Can you pedal the wheel in the air in a work-stand or something by hand
> to figure the aero and drivetrain loss for the back wheel at least?

Good idea. I'll try this.


-Jens

 

[Jens]

I stuck a couple of bikes with SRMs and a powertap on
the trainer today. Turning the wheels at 30mph with no
resistance, here's what I got (measuring power after the
wheel was up to speed)

bike 1:
SRM: 8.3 watts
Powertap: 0 watts.

bike2
SRM: 6.4 watts
Powertap: 0 watts

This was with a mid-section bontrager powertap wheel.


-jens

 

[Ron Ruff]

Jens wrote:
> I stuck a couple of bikes with SRMs and a powertap on
> the trainer today. Turning the wheels at 30mph with no
> resistance, here's what I got (measuring power after the
> wheel was up to speed)
>
> bike 1:
> SRM: 8.3 watts
> Powertap: 0 watts.
>
> bike2
> SRM: 6.4 watts
> Powertap: 0 watts
>
I guess the wheel was free spinning in the air?

If so, it appears that the aero resistance was too low for the Powertap
to measure. I don't know what it's sensitivity or reliability would be
at low power levels. I'd estimate the aero losses at 2-4 watts for one
wheel at 30 mph, depending on the rim and number and type of spokes.

The SRM is at least indicating some resistance... which should be both
drivetrain and aero losses. With an aero "load" of 3 W and an average
input of 7.35 W we get an efficiency of only 40%... this is to be
expected for such a low chain tension, though.

I took a look at Spicer's chain efficiency data, and applied it to your
roller case. With a 53 tooth ring, power input of 120 W, and cadence of
100 rpm (is that close?), I get a chain tension of 107 N, which
corresponds to an efficiency of 88%. In other words your drivetrain
losses would be 14.4 W. With a 240 W input (say, if the front wheel was
also on the rollers) the efficiency would climb to 94%, and the
drivetrain losses (in watts) would stay the same.

If anything, I'd guess that the 15 W number that you are using for all
losses might be a little low... but close.

Have you tried your Crr test a number of times to get a feel for the
repeatability? If so, what kind of scatter did you see?

Also, what diameter rollers do you have?

 

[Jens]

Ron Ruff wrote:
> Jens wrote:
> > I stuck a couple of bikes with SRMs and a powertap on
> > the trainer today. Turning the wheels at 30mph with no
> > resistance, here's what I got (measuring power after the
> > wheel was up to speed)
> >
> > bike 1:
> > SRM: 8.3 watts
> > Powertap: 0 watts.
> >
> > bike2
> > SRM: 6.4 watts
> > Powertap: 0 watts
> >
> I guess the wheel was free spinning in the air?
>
> If so, it appears that the aero resistance was too low for the Powertap
> to measure. I don't know what it's sensitivity or reliability would be
> at low power levels. I'd estimate the aero losses at 2-4 watts for one
> wheel at 30 mph, depending on the rim and number and type of spokes.

I just calibrated the Powertap. Usually Powertaps are right on or
they're way off. It looks like mine is a tiny bit off. For a known
torque
of 321.83 in-lbs, it gave a reading of 320. This may or may not
account for the difference.


>
> The SRM is at least indicating some resistance... which should be both
> drivetrain and aero losses. With an aero "load" of 3 W and an average
> input of 7.35 W we get an efficiency of only 40%... this is to be
> expected for such a low chain tension, though.

Just watching the PT and SRM side-by-side for a while, I can tell you
that drive-train resistance tends to be a lump sum type of deal, it
seems to start at about 6 watts and then scales up to about 10 when
you're really, really hammering. I've never seen it higher than that.

>
> I took a look at Spicer's chain efficiency data, and applied it to your
> roller case. With a 53 tooth ring, power input of 120 W, and cadence of
> 100 rpm (is that close?), I get a chain tension of 107 N, which
> corresponds to an efficiency of 88%. In other words your drivetrain
> losses would be 14.4 W. With a 240 W input (say, if the front wheel was
> also on the rollers) the efficiency would climb to 94%, and the
> drivetrain losses (in watts) would stay the same.
>
> If anything, I'd guess that the 15 W number that you are using for all
> losses might be a little low... but close.
>
> Have you tried your Crr test a number of times to get a feel for the
> repeatability? If so, what kind of scatter did you see?

Totally repeatable, provided I don't slide the front wheel stand around
at all (e.g. to put a different size bike in). If I do that, all bets
are off.

>
> Also, what diameter rollers do you have?

My calipers say 85mm (or 3.35 inches).


--jens

 

[Ron Ruff]

Jens wrote:
>
> Just watching the PT and SRM side-by-side for a while, I can tell you
> that drive-train resistance tends to be a lump sum type of deal, it
> seems to start at about 6 watts and then scales up to about 10 when
> you're really, really hammering. I've never seen it higher than that.
>
That jibes with the drivetrain loss testing I've seen. Maybe the
magnitude is a *little* low, but the loss is pretty constant in watts
over a wide range.

> My calipers say 85mm (or 3.35 inches).

So, I'm getting an equivalent diameter of 2.97 inches and a Crr factor
of 4.59.

P=4.59*1.07(roller separation)*Crr_flat*Mg*V+ 15W

for V in km/hr and M in kg

P=13.4*Crr_flat*M*V + 15W

You determined a 10.8 factor from testing vs the 13.4 that I
calculated. I would have hoped for a closer match, but it really
doesn't surprise me. I don't know how accurate that diameter-scaling
equation is.

Based on your data for the Vittoria, I would calculate:

Crr_flat= (111.4W-15W)/(13.4*46Kg*49.68km/hr) = .00315

This is 80% of what Tour messured for this tire (.0039).

I know Tour used a drum to measure Crr, but I don't know how large it
was, or whether they corrected their values to correspond to a flat
surface. Maybe the number I'm calculating is closer to what you'd get
on a flat, smooth surface... but when you throw in the big unknown
effect of surface roughness on a real road it's going to be higher
anyway... maybe a lot.

> Totally repeatable, provided I don't slide the front wheel stand around
> at all (e.g. to put a different size bike in). If I do that, all bets
> are off.
>

I think it's great that you can get good Crr info from a power meter
and rollers. Maybe other people out there who have this equipment could
do some testing and let us know what they find.

 

[Jens]

Ron Ruff wrote:
> Jens wrote:
>
> Based on your data for the Vittoria, I would calculate:
>
> Crr_flat= (111.4W-15W)/(13.4*46Kg*49.68km/hr) = .00315
>
> This is 80% of what Tour messured for this tire (.0039).
>

Tour tested the tires at 7 bar (or about 100 psi). I did it at
120 psi. There's also the issue of the roller material.


-jens