BikeTechReview.com

  • Increase font size
  • Default font size
  • Decrease font size
Home Forum
Welcome, Guest
Username Password: Remember me

Help a physics student out.
(1 viewing) (1) Guest
  • Page:
  • 1

TOPIC: Help a physics student out.

Help a physics student out. 4 years ago #27121

  • howardjd
  • OFFLINE
  • Senior Boarder
  • Posts: 41
  • Karma: 0
If anyone happens to have a value for their Cda, avg power and velocity for a typical flat course, and crr for tires used, along with rider mass, if you would be willing to share would be greatly appreciated.

I recently constructed a Virtual Instrument in Lab View a graphical programming software for modeling bicycling. It is based on a kinetic energy model. It has the following inputs.

wheel inertia
Mass rider and bike
power (as a sinusoidal function if desired)
the input of a hypothetical course profile generated by a sinewave(the parameters to the sine wave can be adjusted to change the course type, like short steep hills, long gradual hills, ext)
Cda
air density
ext

I tested it with my own numbers and it produced a good value for my flat course steady state velocity and I also generated a course profile to approximate a rolling course I frequently ride and it gave me a good avg velocity value.

So if anybody would has and is willing to share their numbers it would be greatly appreciated and would help me out a lot in testing out my model. To make it more fun you could hold off on giving me your normal steady state velocity, provide me with the other info, then I could report back without knowing what the "correct answer" should be.

Today I'm going to run some tests with it to see what bike riding on the moon, mars, titan, mercury, and venus would (approximately) be like.
Last Edit: 4 years ago by howardjd. Reason: grammar

Re: Help a physics student out. 4 years ago #27122

  • kraig
  • OFFLINE
  • Administrator
  • Posts: 3285
  • Karma: 4
If you search the forum for "crr field testing" I think you'll find CxA and Crr for me on my road bike. all-up mass was probably 78kg or so.
-kraig

Re: Help a physics student out. 4 years ago #27123

  • howardjd
  • OFFLINE
  • Senior Boarder
  • Posts: 41
  • Karma: 0
So for the first set of data you had at 120 psi using 250watts with your CxA=0.351, crr=0.0067, leaving out wheel intertia for now as getting steady state velocity, and using a air density of 1.2. I get

22.1mph

second trials at 90psi CxA=0.357 crr=0.0059 at 250 watts air density 1.2 I get

22.2mph

third set of trials at 140 psi CxA=0.349 crr=0.00609 at 250 watts air density 1.2 I get

22.3mph


I used an arbitrary wattage and estimated air density. If you could provide me with your wattage, altitude, and the approximate temperature of testing I could run it again with better values for both the wattage and air density.

Thanks for the info.

Just for fun I calculated that on the moon If I had a Crr of 0.005 and neglected bearing resistance and I pedaled steady at 300watts in 16 hours I could reach 800mph. On Venus I would only be able to reach a velocity of 7mph for 300watts 0.005 crr, on Mars 70mph 300watts 0.005 crr.

Re: Help a physics student out. 4 years ago #27124

  • howardjd
  • OFFLINE
  • Senior Boarder
  • Posts: 41
  • Karma: 0
Well I've been doing a lot of analysis with my Virtual Instrument lately and come up with some interesting findings. First from the model I created I was wrong that rpm and power fluctuations over the pedal stroke have any significant effect on performance(except in limiting cases of very low rpm's and high power amplitude), larger wheel inertia does not seem to show a positive benefit in any circumstance. Now the interesting stuff.

1. For rolling courses without long climbs a wheel with a greater inertia(I simulated inertia changes by adding hypothetical mass to the rims) you will be less slow than on a flat course.

2. On a rolling course adding mass to the rims produces less loss than adding mass to the bike or rider.

3. Tire selection is more important than wheel mass, take for example this hypothetical example

of a course with hill peaks separated by 6400m and that rise to 150m.

run 1
300watts, 1.2 air density, .27 cda, .003 crr, wheels with 500gram rims.

25.6mph

run 2 300watts, 1.2 air density, .27cda, 0.003 crr, wheels with 5kilogram rims

25.51mph

run 3 300 watts, 1.2 air density, 0.27cda, 0.0035 crr, wheels with 500 gram rims

25.43 mph

So just having wheels different by just .0005 in crr is produces more loss than if you added a full 20+pounds total to the rims of your wheels.

Now all this depends on the accuracy of my model.

note: this analysis is geared towards steady state riding found in time trial and triathlon.
Last Edit: 4 years ago by howardjd.

Re: Help a physics student out. 4 years ago #27125

  • kraig
  • OFFLINE
  • Administrator
  • Posts: 3285
  • Karma: 4
sounds like a fun project! How are things compared to the model developed here:

biketechreview.com/index.php/reviews/whe...63-wheel-performance
-kraig

Re: Help a physics student out. 4 years ago #27126

  • howardjd
  • OFFLINE
  • Senior Boarder
  • Posts: 41
  • Karma: 0
My model was a kinetic energy based model that used a while loop to compute incremental steps over a chosen distance and course profile. It went as follows.

Kinetic energy new= the newly calculated kinetic energy
kinetic energy old= is the calculated kinetic energy from the previous iteration of the loop
to incorporate intertia into the model I made a input for Inertia(I) that really just meant mass added to the rim the
mass = mass rider and bike
power= power input of the rider
aero drag force = .5*Cda*air density * velocity_old^2
force rolling resistance = mass * 9.8 * crr*velocity_old
dt = the user input time step I stuck with .1 second

since the rolling resistance depends on the normal force which is affected by the slope and change in curvature I'm working on making this more exact. The way I have it now approximates that over a hilly course the rolling resistance will average to about the same as a flat course.

I solved for kinetic energy new as

kinetic energy new =kinetic energy old + Power * (dt) - Aero Drag force * velocity_old * dt -
(force rolling resistance * velocity_old *dt) -
( sin(arctan(slope course))*g*(mass + I)*velocity_old*dt)

to get the new velocity for each iteration of the loop I solved kinetic energy = .5 total mass velocity_old^2 + .5 *inertia*(angular velocity)^2 to get

Velocity new = sqrt((2 * (kinetic energy new))/(mass + 2I)) remember I is not the inertia but the mass added to the rims.

So the way I have it programmed now when I adjust the inertia I am assuming I am adding mass to the rims. With a little manual adjustment I can also simulate inertia from disk wheels.

To generate the course I made a sine wave as
Amplitude * sin( (2 * pi * distance traveled)/peak to peak distance))
the total height of the simulated hills is two times the amplitude. To get the slope for the calculation of the power loss or gain from gravity simply take the derivative.

the distance traveled that goes into an input to the sine wave I simply took
distance traveled + velocity_old * dt.

the while loop end by the condition that the distance traveled was greater than the user input for the distance for the simulation.

the data was plotted to an xy graph of velocity vrs time or distance if you so choose. I had an indicator for the average velocity over the course.

I only have access to the software at school and I'm out of town for the weekend but when I get back on Monday I'll try and make predictions for the same scenarios listed in your section on wheel performance and see what I get.
Last Edit: 4 years ago by howardjd.

Re: Help a physics student out. 4 years ago #27128

  • howardjd
  • OFFLINE
  • Senior Boarder
  • Posts: 41
  • Karma: 0
Void this info I found a fault in my program. I re-ran the example profile in finding three on the given course with the corrected program and it predicted the wheels with 5kilo rims would be about 1/10th a mile per hour slower than the tires that where .0005 higher in crr but with the same mass wheels.



howardjd wrote:
Well I've been doing a lot of analysis with my Virtual Instrument lately and come up with some interesting findings. First from the model I created I was wrong that rpm and power fluctuations over the pedal stroke have any significant effect on performance(except in limiting cases of very low rpm's and high power amplitude), larger wheel inertia does not seem to show a positive benefit in any circumstance. Now the interesting stuff.

1. For rolling courses without long climbs a wheel with a greater inertia(I simulated inertia changes by adding hypothetical mass to the rims) you will be less slow than on a flat course.

2. On a rolling course adding mass to the rims produces less loss than adding mass to the bike or rider.

3. Tire selection is more important than wheel mass, take for example this hypothetical example

of a course with hill peaks separated by 6400m and that rise to 150m.

run 1
300watts, 1.2 air density, .27 cda, .003 crr, wheels with 500gram rims.

25.6mph

run 2 300watts, 1.2 air density, .27cda, 0.003 crr, wheels with 5kilogram rims

25.51mph

run 3 300 watts, 1.2 air density, 0.27cda, 0.0035 crr, wheels with 500 gram rims

25.43 mph

So just having wheels different by just .0005 in crr is produces more loss than if you added a full 20+pounds total to the rims of your wheels.

Now all this depends on the accuracy of my model.

note: this analysis is geared towards steady state riding found in time trial and triathlon.
  • Page:
  • 1
Time to create page: 0.69 seconds

Poll

Which type of tire is more aerodynamic?