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What's the "virtual" CdA and Crr of the LeMond Revolution?

 

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Tom A.

Jan 28, 11 15:51

Post #1 of 30 (7845 views)
What's the "virtual" CdA and Crr of the LeMond Revolution? Quote | Reply

That's a question I've been interested in quite awhile...and with my getting access to one recently, I decided to run a few tests/analyses.

Just in case anyone besides me was interested, here's the result of a constant cadence cassette sweep (only 9 of the 10 cogs of a 12-25 cassette, 60 rpms, with a repeat of the 53-14 at 75 rpm for some slightly higher power.) After the sweep, I did some accelerations/decelerations for the purposes of doing some inertial mass estimates (more on that later).



Taking the average of the power and "virtual speed" (i.e. the result of the gearing, cadence, and assumed wheel rollout) over the last 2 minutes of each step (and the last 1 minute of the 75 rpm step), I then plotted P/V vs. V^2 for the following:



Assuming an "all-up" mass of 85kg, and a rho of 1.2 kg/m^3, that y-intercept works out to represent a Crr = .0051 and the slope of the line works out to represent a CdA = .350 m^2. Sounds like a fairly "normal" road bike position (on the hoods) and Crr.

Now...about that estimate of inertial mass. My intent was to plug the file and the calculated Crr and CdA into my VE spreadsheet and then modify the mass entry until the small "hills" formed by the accelerations/decelerations "flatten out"...I tried that, but I think I need to reconsider how varying the mass entry affects the calculated rolling resistance force (I might need to separate out the mass terms used for the rolling resistance calcs and the other places the mass term is used). Although, with an assumed 85kg mass, it's pretty darned flat as it is. (I actually had to slightly increase the CdA to .353 to flatten out the "steps")



I think I might just pull the fan/flywheel cover off and measure up the flywheel and just manually calculated the moment of inertia ;)


http://bikeblather.blogspot.com/

(This post was edited by Tom A. on Jan 28, 11 16:04)


RChung

Jan 28, 11 16:10

Post #2 of 30 (7829 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:

What happens if you accelerate more gently and then coast down (e.g., make the speed trace look like a triangle)?


Tom A.

Jan 28, 11 16:22

Post #3 of 30 (7813 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
Tom A. wrote:


What happens if you accelerate more gently and then coast down (e.g., make the speed trace look like a triangle)?

Here's what the speed trace looks like from the accel/decel section...I guess I accelerated faster than I'd thought. My intent was to give it a big "signal"...but yeah, maybe I need to be a bit more gentle...




http://bikeblather.blogspot.com/


RChung

Jan 28, 11 17:04

Post #4 of 30 (7789 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:
Here's what the speed trace looks like from the accel/decel section...I guess I accelerated faster than I'd thought. My intent was to give it a big "signal"...but yeah, maybe I need to be a bit more gentle...

Can you overlay the VE on that speed trace?


bazilbrush

Jan 28, 11 17:22

Post #5 of 30 (7773 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Is this thread available in English?


JustinPB

Jan 28, 11 17:49

Post #6 of 30 (7757 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

awesome. I love this stuff. I've been playing with this with my KK since I got a powermeter. I'm going to have to "Chung" myself once i get a free saturday.


Tom A.

Jan 28, 11 17:58

Post #7 of 30 (7748 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
Can you overlay the VE on that speed trace?

Like this?




http://bikeblather.blogspot.com/


Tom A.

Jan 28, 11 18:10

Post #8 of 30 (7737 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [bazilbrush] [In reply to] Quote | Reply

bazilbrush wrote:
Is this thread available in English?

Sure...quick translation...I wanted to quantify just how close the Revolution "mimics" riding outside and this thread is showing how I'm doing that. So far, the "load curve" of the Revolution appears to match VERY well the "typical" aero drag and rolling resistance of riding your road bike outside on perfectly level ground. I was able to determine this using the same method one would use to field test to determine aero drag and rolling resistance outside using a power meter.

The last piece of the puzzle is determining how well the flywheel "mimics" the inertial mass of a rider+bike traveling down the road at the same indicated speed. I tried doing that using Robert's VE technique and the coefficients measured above. That's what Robert and I are going back and forth about...

Up to speed? ;-)


http://bikeblather.blogspot.com/


RChung

Jan 28, 11 20:42

Post #9 of 30 (7698 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:


Aha. Excellent. It may "coast" better than regular trainers -- but not as well as a bike on a flat road. Likewise, it appears to accelerate faster than a bike on a real road. Steady state load is reasonable, though.


RChung

Jan 29, 11 7:09

Post #10 of 30 (7631 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
Tom A. wrote:




Aha. Excellent. It may "coast" better than regular trainers -- but not as well as a bike on a flat road. Likewise, it appears to accelerate faster than a bike on a real road. Steady state load is reasonable, though.

I presume you were using an all-up mass of around 80kg? So cut that in half to 40kg and double the Crr to .01. That'll keep the steady state power the same but should improve the modeling for the KE component.


uberslug

Jan 29, 11 12:53

Post #11 of 30 (7552 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

Doesn't anyone just ride their bike anymore?
I know enough to know I don't know enough...


JustinPB

Jan 29, 11 12:54

Post #12 of 30 (7551 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [uberslug] [In reply to] Quote | Reply

why do you have to be an ass?


uberslug

Jan 29, 11 16:35

Post #13 of 30 (7499 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [jpb] [In reply to] Quote | Reply

jpb wrote:
why do you have to be an ass?

I believe it was Lao Tzu who wrote "To become learned, each day add something. To become enlightened, each day drop something." So, in that vein, I am considering moving past the gaining of knowledge through the use of power meters and embracing a more zen like approach to training.

In looking back at my wording, I can see where my question could be misinterpreted. Mea maxima culpa...
I know enough to know I don't know enough...


Tom A.

Jan 29, 11 17:24

Post #14 of 30 (7487 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
I presume you were using an all-up mass of around 80kg? So cut that in half to 40kg and double the Crr to .01. That'll keep the steady state power the same but should improve the modeling for the KE component.

Yeah...I thought of the same thing last night. Just modify the Crr to compensate for changing the mass so that the rolling resistance force stays constant. I just haven't had a chance yet to try that....


http://bikeblather.blogspot.com/


Sausagetail

Jan 29, 11 18:16

Post #15 of 30 (7476 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [uberslug] [In reply to] Quote | Reply

I thought this was the most interesting thread in the past week or two...


RChung

Jan 29, 11 19:19

Post #16 of 30 (7461 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Sausagetail] [In reply to] Quote | Reply

Sausagetail wrote:
I thought this was the most interesting thread in the past week or two...
Lemond is selling their "Power Pilot" for, what, $400+? With Tom's info, you can print out the cadence-gear-power combos on an 8-1/2" x 11" sheet of paper and scotch tape it to the wall. Send 10% of the savings to Tom.


Tom A.

Jan 29, 11 20:07

Post #17 of 30 (7444 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
Sausagetail wrote:
I thought this was the most interesting thread in the past week or two...

Lemond is selling their "Power Pilot" for, what, $400+? With Tom's info, you can print out the cadence-gear-power combos on an 8-1/2" x 11" sheet of paper and scotch tape it to the wall. Send 10% of the savings to Tom.

...except that doesn't provide one with a downloadable record of the session ;-)


http://bikeblather.blogspot.com/


RChung

Jan 29, 11 21:20

Post #18 of 30 (7423 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:
RChung wrote:
Sausagetail wrote:
I thought this was the most interesting thread in the past week or two...

Lemond is selling their "Power Pilot" for, what, $400+? With Tom's info, you can print out the cadence-gear-power combos on an 8-1/2" x 11" sheet of paper and scotch tape it to the wall. Send 10% of the savings to Tom.


...except that doesn't provide one with a downloadable record of the session ;-)
Work with me.


VO2Matt

Jan 30, 11 9:58

Post #19 of 30 (7364 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:
RChung wrote:
Sausagetail wrote:
I thought this was the most interesting thread in the past week or two...

Lemond is selling their "Power Pilot" for, what, $400+? With Tom's info, you can print out the cadence-gear-power combos on an 8-1/2" x 11" sheet of paper and scotch tape it to the wall. Send 10% of the savings to Tom.


...except that doesn't provide one with a downloadable record of the session ;-)

So use a computer that logs cadence and rear wheel speed. It's simple spreadsheet math from there.


sometimes you just have to eat the cake


Tom A.

Jan 31, 11 14:56

Post #20 of 30 (7214 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
RChung wrote:
Tom A. wrote:




Aha. Excellent. It may "coast" better than regular trainers -- but not as well as a bike on a flat road. Likewise, it appears to accelerate faster than a bike on a real road. Steady state load is reasonable, though.


I presume you were using an all-up mass of around 80kg? So cut that in half to 40kg and double the Crr to .01. That'll keep the steady state power the same but should improve the modeling for the KE component.

Here's the "best fit" I could find...and I mostly judged it off of the final "tail" which was a coast down to zero rpm. I adjusted the mass (and Crr accordingly) until the final steady-state leg and the coast down to zero had a minimum of "disjoint". This case was actually 100 lbs (45.5 kg) and a Crr of .0094



Now...we'll see how close that is to a calculated mass based on the flywheel geometry!


http://bikeblather.blogspot.com/


atopham

Feb 7, 11 5:51

Post #21 of 30 (7088 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

So I'd love to be able to evaluate all this myself but my head starts to hurt when I try. I have a Kurt Kinetic right now and it is an awesome piece of kit, with a very long coast down from, say 20 mph, of over a minute. But that vstill leaves me pushing 15% less power through it than I can on the road in the TT position. So can you tell me what the coastdown time would be from 20 mph on the Lemond?
Cheers.
http://www.timetrialling.com
TT is like stubbing your toe very hard. It's self inflicted, it's stupid and it REALLY hurts!!


Tom A.

Feb 11, 11 20:12

Post #22 of 30 (7002 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:

Now...we'll see how close that is to a calculated mass based on the flywheel geometry!

Had a chance today to pull the flywheel cover off and measure up the flywheel on the trainer. Decided to just throw the dimensions into Pro/E and let it do the moment of inertia calculations:



Here's the mass properties output:
Quote:
VOLUME = 8.0428750e-04 M^3
SURFACE AREA = 2.0893183e-01 M^2
DENSITY = 7.8887728e+03 KILOGRAM / M^3
MASS = 6.3448414e+00 KILOGRAM

CENTER OF GRAVITY with respect to _GL_FLYWHEEL coordinate frame:
X Y Z 0.0000000e+00 0.0000000e+00 2.4937030e-02 M

INERTIA with respect to _GL_FLYWHEEL coordinate frame: (KILOGRAM * M^2)

INERTIA TENSOR:
Ixx Ixy Ixz 4.2069766e-02 0.0000000e+00 0.0000000e+00
Iyx Iyy Iyz 0.0000000e+00 4.2069765e-02 0.0000000e+00
Izx Izy Izz 0.0000000e+00 0.0000000e+00 7.3130437e-02

INERTIA at CENTER OF GRAVITY with respect to _GL_FLYWHEEL coordinate frame: (KILOGRAM * M^2)

INERTIA TENSOR:
Ixx Ixy Ixz 3.8124192e-02 0.0000000e+00 0.0000000e+00
Iyx Iyy Iyz 0.0000000e+00 3.8124191e-02 0.0000000e+00
Izx Izy Izz 0.0000000e+00 0.0000000e+00 7.3130437e-02

PRINCIPAL MOMENTS OF INERTIA: (KILOGRAM * M^2)
I1 I2 I3 3.8124191e-02 3.8124192e-02 7.3130437e-02

ROTATION MATRIX from _GL_FLYWHEEL orientation to PRINCIPAL AXES:
1.00000 0.00000 0.00000
0.00000 1.00000 0.00000
0.00000 0.00000 1.00000

ROTATION ANGLES from _GL_FLYWHEEL orientation to PRINCIPAL AXES (degrees):
angles about x y z 0.000 0.000 0.000

RADII OF GYRATION with respect to PRINCIPAL AXES:
R1 R2 R3 7.7515746e-02 7.7515748e-02 1.0735906e-01 M

The value we're interested in is the the Izz value of .073 kg*m^2.

So...how do we equate this to an "equivalent mass" translating down the road? I like to do it by equating the kinetic energy of the flywheel to the kinetic energy of a bike+rider moving down the road.

Kinetic Energy of rider = Kinetic Energy of the Flywheel
KErider = KEf
1/2 x mass of rider x (velocity of bike)^2 = 1/2 x Izz x (flywheel rotational speed)^2
Mr x Vb^2 = Izz x (Wf)^2

OK...to solve this, I need to equate the flywheel rotational speed (in radians per second) to the equivalent bike velocity (in meters/second). Well, the assumption above was that the wheel rollout was 2080mm, or 1 revolution = 2*Pi radians is equivalent to 2080mm of rollout.

Wheel rotation rate = Ww = Vb x (2*Pi radians/2.080m), where Vb is in m/s, so Ww = 3.0208 x Vb.

Now, to figure the flywheel rotational rate, we need to know the pulley ratio of the drive pulley and the flywheel pulley. By my measuring, this ratio is 8:1. So, the flywheel rotational rate, Wf = 8 x Ww = 8 x 3.0208 x Vb = 24.166 x Vb.

Lastly, I'll plug this relation into the simplified KE equation above along with the calculated Izz from the solid model.

Mr x Vb^2 = Izz x (24.166 x Vb)^2
Mr = Izz x 584 = .073 x 584 = 42.6 kg

42.6 kg is equivalent to a rider weight of ~94 lbs...now, that's also not including the other rotating bits (like the pulleys, cassette, etc.)...but that's pretty darned close to the "equivalent mass" determined using the coastdown and VE above :-D


http://bikeblather.blogspot.com/


bpq

Feb 11, 11 20:22

Post #23 of 30 (6991 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Nice. I've gone to the dark side and now work for sales. I miss Pro-E.


RChung

Feb 11, 11 20:27

Post #24 of 30 (6987 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [Tom A.] [In reply to] Quote | Reply

Tom A. wrote:
...but that's pretty darned close to the "equivalent mass" determined using the coastdown and VE above :-D



Tom A.

Feb 11, 11 20:28

Post #25 of 30 (6985 views)
Re: What's the "virtual" CdA and Crr of the LeMond Revolution? [RChung] [In reply to] Quote | Reply

RChung wrote:
Tom A. wrote:
...but that's pretty darned close to the "equivalent mass" determined using the coastdown and VE above :-D



Hehehe...I actually was going to put that at the end of the post, but forgot. Thanks!


http://bikeblather.blogspot.com/

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