I'm really into motorcyle physics lately as a result of lurking on this forum. My area of interest right now is braking. I'd like to take everything very slowly and see if my results are right as a relationship wasn't borne out by testing. I'm studying Motorcycle Dynamics by Cossalter. I would like to be sure I'm getting each small step.
Could you please check this diagram for accuracy. Thanks.
Edited by - galileo on 08/24/2009 5:07 PM
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/23/2009 : 7:49 PM
We will certainly help you, but you need to tell us more with your request than what you have asked. You showed us a diagram with some dimensions. So?
Though I know what Cossalter labels his dimensions, but why would you expect others to?
I can tell you that 'p' in your diagram is wrong. Presumably you want to show wheelbase. That is NOT the distance between the axles. Instead, it is the distance between the center of the contact patches. Further, your diagram shows the rear part of the dimension to the right of the center of the axle (and center of the contact patch).
galileo Ex-Member
Posted - 08/23/2009 : 8:07 PM
James,
Thank you for your reply. I had the same question as you about p. On Page 98, Cossalter shows the normal forces acting on the axles. Any deviation from that from my picture is accidental. Personally, I'd put p as the wheelbase also.
As a hint to where I'm going, I decided to calculate the height of the CG through brake testing and came up with an impossible number. I'd like to go through my method.
Here is an updated diagram I hope is acceptible. If you like, I'll change the original, also.
gdickelman Moderator
1191 Posts
[Mentor]
Annandale, VA
USA Moto Guzzi
California Vintage
Posted - 08/23/2009 : 9:53 PM
quote:Originally posted by galileo
James,
Thank you for your reply. I had the same question as you about p. On Page 98, Cossalter shows the normal forces acting on the axles. Any deviation from that from my picture is accidental. Personally, I'd put p as the wheelbase also.
As a hint to where I'm going, I decided to calculate the height of the CG through brake testing and came up with an impossible number. I'd like to go through my method.
Here is an updated diagram I hope is acceptible. If you like, I'll change the original, also.
I'm with James...same question: What are you asking? You are showing a motorcycle with some dimensions marked. Perhaps you could give us a riding and braking scenario, then tell us what you want to know about the labeled dimensions or forces or whatever they are supposed to be.
galileo Ex-Member
Posted - 08/23/2009 : 11:38 PM
One more, then it's really time for bed. I put a scale under the front wheel of my bike with me on it. The weight on the front wheel was 309 pounds. The wheelbase is 64 inchs.
Then I computed the values for p, b and p-b and Nr. Here is what I ended up with. Notice h is still unknown.
I used the equations:
Nf = mg*b/(p) and Nr=mg*(p-b)/p
If someone would like to check my work, I'd appreciate it.
Gdickelman, without an understanding of this part, it will be impossible to answer te question I have. It will be faster to go slowly at first. Thanks for your patience.
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/24/2009 : 6:29 AM
Shall we get serious here, please?
You can show off your artistic ability if you want, but we are not a community of artists so the odds are that you are not asking us for composition critique.
Many of us ARE well versed in practical physics and math, but you have, so far, merely asked us if your simple multiplication and divide results are correct. Further, you insist that we need to 'understand' those multiplication and divide results before we can help you.
That is so condescending as to be a put off to many of us. Get on with it, already!
By the way, your third diagram shows two force vectors. The vertical one is obvious, but the horizontal one is meaningless as there is no context for it, nor dimensions.
galileo Ex-Member
Posted - 08/24/2009 : 8:32 AM
James,
I agree that the horizontal vector at the CG is meaningless for now. Please consider it deleted. Thanks for pointing that out. It will be added later.
Sorry for sounding condescending. I know you know the physics. That's why I'm here. I'm trying to get some confirmation that I understand the physics correctly. I've been working on this for about 6 weeks, and I've come to the conclusion I may have an error someplace. Or that the practice isn't matching a simplified theory. I think it is the second.
My conclusion will be to suggest a braking exercise which will develop a feel for the maximum rear braking to be used in threshold braking to prevent a rear wheel skid. It will also suggest a braking exercise that can be done to learn the balance of braking required on a wet surface. From this, I will suggest a habit pattern to be used in normal braking so that threshold braking is a natural extension of normal braking.
Added: It may be possible to also suggest a means to adjust the brake pedal so that point of maximum use of the rear brake is easily found.
Before suggesting something that may be wrong, I want to be absolutely certain that my understanding of the theory is correct.
In order to help understand the theory, I went out and did a braking test. First I did about 20 repetitions of braking with just the rear wheel. All of them were from 18 mph. I got to the point where I was able to leave an incipient skid for the entire length of the braking, so I knew I was close to maximum braking available with just the rear brake.
I did the same with front only and then front and rear.
I approached the limits very carefully, and in 60 braking tests, I never experienced a skid on either wheel.
Here are my results:
Rear only: 29.2 Feet. Deceleration to be .37 g's. Front only: 20.2 Feet. Deceleration = .54 g's Front and rear: 16.2 Feet. Deceleration = .67 g's (Which also equals the Cf.
To determine the stopping deceleration, I used the equation:
m(a/g)d = 1/2 mv^2
The mass cancels out. Rearringing things, I get:
a=.5 v^2/(d*32.2)
For both brakes from 18mph (26.4 fps), I found this for using both brakes.
a=.5*26.4^2/(16.2*32.2)
a=.67 (Equal to CF since both brakes were used.)
From these, I concluded it may be possible to compute the height of the CG (h) relative to p (wheelbase.) (This is where my theory breaks down.)
If this meets with approval, I'll show why this is important.
Edited by - galileo on 08/24/2009 9:05 AM
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/24/2009 : 9:13 AM
A casual review of what you posted is encouraging.
I take issue with your twice asserting that the CF is 0.67, however, in that nowhere have you demonstrated that to be a known fact and I doubt that you mean what you think you mean when you make that claim.
That is, I wonder if you mean to suggest that the CF is the static or the dynamic CF? I find from experience that the dynamic CF of most roadway surfaces is in excess of 0.8 and I would be surprised to learn that the dynamic CF of a parking lot is below 0.7, though that is certainly possible. On the other hand, sliding (the loss of traction) occurs as you exceed the static CF, not the dynamic CF. Since the static CF is usually about 25% greater than dynamic CF (or dynamic CF is usually about 20% lower than static, your deceleration rate of 0.67 should not be an indication of threshold braking but, rather, normally aggressive braking.
galileo Ex-Member
Posted - 08/24/2009 : 10:53 AM
James,
I'm thinking what you are saying is my braking has room for improvement. Would I be correct in saying the deceleration I am actually achieving is expressed by the equation:
mg*u*BE=ma g*u*BE=a
where BE is braking efficiency.
The letter that sounds like you is the static coeficient of friction. (The grammar checker won't let me type the letter by itself.)
The parking lot is relatively new and smooth. My tires are almost at the time to replace and I plan to use the rest of the tread in braking practice.
I think the next statement is right. If indeed, CFstatic=1 then I'm at 67% braking efficiency. If that's true, I'd certainly like help in improving it.
Your post made me think of another experiment. I'd like to reduce the preload on my rear shocks to the middle range and then to the minimum and see how that affects the braking. Right now it's at the maximum as that's where the ride feels most comfortable. My prediction is that will increase my braking distance for the method I'm currently using as it will slow the rate at which the weight is transferred.
I'm thinking that the area to improve is in handling the transition time during which weight shift occurs as I am really quite close to a skid on both wheels once I achieve equilibrium. During the transition point, neither wheel is close to a skid. This is based on my perception and not a scientific analysis.
I'd also like to do an experiment to determine the dynamic coefficient of friction. Would crossing the start line at 18 mph in neutral and determining the distance it takes to slow to a stop give this to me?
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/24/2009 : 11:01 AM
Create a drag sled from a piece of weighted motorcycle tire and, using a scale, determine how much of that weight is required to skid the tire along the roadway.
If you want to reference a symbol, put it in parenthesis as in 'u'.
Since you are trying to determine the height of the bike's CG (including yourself), and you can measure the weight on each of the tires, all you need to do is lift one end of the bike and then measure the new wheelbase and new weights on those tires.
galileo Ex-Member
Posted - 08/24/2009 : 3:00 PM
(Edited to correct height. This post is still not the final answer as the CG's don't match.)
If I were Archimedes, I'd be shouting Eureka and running down the street naked. But, alas, I'm Enrico Galileo. I don't know what he did. Hopefully nobody caught the picture that was up here briefly. There was a little error. I had to make a second correction as I had put some bad numbers in the spreadsheet. But now, the CG comes out at a very reasonable 25 inches. Along with running naked, I'm eating a little crow, too.
After doing this, I think it's possible to write a spreadsheet to handle the general case for any bike. All a person would need to know is the wheelbase of the bike and I think everything can be calculated from a rear braking braking exercise. From this, it will be able to be determined if a bike might do a stoppie. If so, the next part might not be safe.
From this information, I think I can devise a practical braking exercise to improve stopping performance.
If we can confirm this, I'd be happy to contribute the spreadsheet to the forum.
Meanwhile, I'm going to go try the tests with the ABS on and see what I get.
Edited by - galileo on 08/25/2009 3:37 PM
galileo Ex-Member
Posted - 08/24/2009 : 3:42 PM
If possible, maybe an admin could change the title of this thread to something like "Motorcycle Braking Dynamics"
greywolf Advanced Member
682 Posts
[Mentor]
Evanston, IL
USA Suzuki
DL650AK7
Peer Review:
1
Posted - 08/24/2009 : 8:45 PM
quote:Originally posted by galileo
I'd like to reduce the preload on my rear shocks to the middle range and then to the minimum and see how that affects the braking
Be careful you don't go outside the limits of proper sag settings when changing the preload. With you sitting on the bike at 0mph and only the wheels on the ground, you want the shock to use 25-35% of its travel. See http://www.vstrom.info/Smf/index.ph...,7132.0.html for how to check. Otherwise, you risk topping out or bottoming out the suspension. Now back to your regularly scheduled program.
galileo Ex-Member
Posted - 08/25/2009 : 7:39 AM
Finally, it's time to present a preliminary conclusion. I'd have done this at the beginning, but at then, I only had a vague idea that this existed. Now, I'm prepared to suggest an action for experienced riders to try and get back to me with the results.
I stayed up most of the night checking the math on this and I'm pretty sure it is correct. Hopefully, experimentation will show this to be so.
Here is the application.
Get the wheelbase from the owner's manual, and measure the weight on the front wheel with the rider on the bike. Then do 3 braking exercises.
1. Find the shortest distance you can stop with just the rear brake. 2. Find the shortest distance you can stop with just the front brake. 3. Find the shortest distance you can stop with both brakes.
The first determines the height of the CG. The combination of the first two determines the Coeficient of Friction. The third determines your braking efficiency.
Enter the data in the brown.
The table on the bottom shows the balance of braking during maximum braking. I have a very low CG, so the contribution of the rear wheel is relatively high. These will be different for different bikes.
The next step is to learn the feel for the pressure on each brake that will be used during threshold braking.
Using the yellow cells, starting at the top.
Practice stopping in the distance for the rear brake using just the rear brake and just a single pressure for the whole time. (This will be different for every bike/rider combination.) Do this until you have a good feel for your foot position and the pressure needed.
Then do the same with the front brake.
Combining the two pressures will theoretically give the stopping distance for both. The amount you exceed it will be a measure of braking efficiency.
I'm hoping to develop some sort of data table so that the program won't be needed.
I won't consider this method of learning to brake to be effective until I've gone out and tried it on all 6 of my bikes and it results in improving my stopping distances. I also need to find other experienced riders to test the theory to see if it works.
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/25/2009 : 2:50 PM
Before you go waltzing off to another bit of 'fun' (for you), how about justifying or at least explaining your methodology?
For example, as I asked before, how did you determine the CF to be 0.86?
Do you typically run on after burners when you work out a problem? Is that why your diagram still shows the height of the CG to be an unreasonable 36.2?
We can work with you if it's a two-way street, but it would appear that you want to flash your work product and dash off to another problem without engaging us. Bet that stops before you get too much further into this site.
galileo Ex-Member
Posted - 08/25/2009 : 3:26 PM
James,
Sorry about waltzing off. I'll hold back on that thread. If you like, I'll delete it. I don't see it leading anywhere useful anyway.
Keep in mind, I believe you are the most capable person on the internet in motorcycle physics. Certainly the most capable who will communicate in a forum where so many can catch errors.
I'm willing to continue with just this thread as long as you wish. Especially as long as you catch errors. I'd like the end result to be as good as possible. If you like, you can have the program when it's done. The results might be useful for learning braking.
There is an error in a picture on a previous post. Sorry about that. I'll go back and fix it as soon as I can. It should just be 'h' as it was unknown at that time.
Initially, I took .86 from one of your examples. I figured it was close enough. As it turned out, it wasn't as small differences change the height of the CG by more than I was satisfied with.
I made the assumption that if the equations can predict the performance given the right variables, then the performance can solve for the variables. I realize there will be some inaccuracies as the test isn't perfect. But let me explain how I got the .853 in the final result.
In the first test I found the deceleration to be .37 g's using just the rear tire. I think I'm correct in stating that the force must have been 271 lb. From this, I determined the weight transfer must have been 104 pounds. Then I determined h/p using the equation
Ntr = Fr(h/p)
I did the same for the front tire, but then there was a problem as it calculated different heights for the CG.
I concluded there is only one value for the coefficient of friction that would make the cg's the same. There is an elegant simultaneous equation for this, but I'm more brute force. I used an iteration to gradually increase the CF until both the Cg's were the same.
Yes, there will be inaccuracies, and I want to go test the practice method to see if it works.
If you'd like the excel program, I can send it to you. It does contain a macro which I can delete before sending it if you wish.
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/25/2009 : 4:00 PM
I don't recall, ever, using 0.86 as a measured static CF. I have seen many instances of a dynamic CF of that or nearly that.
We can certainly accept errors here so long as they are clearly a part of a work in process and are not delared to be facts.
First blush review:
Your front brake only deceleration rate is too low to be meaningful. A deceleration rate of 0.57 is below the deceleration rate expected of even a rank amateur (when using both brakes) but since the bike you appear to be testing is a sport bike and they are usually capable of doing stoppies where 100% of braking performance comes from the front brake, I would expect something much higher than 0.57 g's.
It is not possible for you to determine the CF from the information you have provided. If the CF was 2.0 your results could be exactly the same as they, in fact, demonstrate the braking performance of the rider more than they demonstrate limits.
galileo Ex-Member
Posted - 08/25/2009 : 4:39 PM
James,
I'm not sure if you want to get involved in this by doing some testing. It would quickly prove or disprove my method. I'm under the impression you know the CG of your bike/rider combination. If you give me just the data in the brown boxes of the program, let's see how close I get. Meanwhile, I'll see if I can get the equipment to accurately measure the height of my CG. I understand the method, but I don't have a jack and I just discovered I broke my scale.
Meanwhile, I think I need a brake (sic) from this for a bit.
James R. Davis Administrator
14930 Posts
[Mentor]
Houston, TX
USA Honda
GoldWing 1500
Posted - 08/25/2009 : 4:57 PM
I do not want to get involved by doing tests. Since I last bothered to calculate the location of my CG I have changed bikes and have been perfectly satisfied that my measurement technique works from the first effort.
Let's work on your numbers instead of mine.
galileo Ex-Member
Posted - 08/25/2009 : 5:02 PM
Ok. It will probably take me until at least this weekend to get a new scale and a way to accurately measure everything. Thanks for your patience.
galileo Ex-Member
Posted - 08/26/2009 : 8:48 AM
James,
I don't know if you find this discussion interesting. If not, please let me know and I'll stop. If so, I'm happy to continue here. Either way, know that I'm very appreciative of your inputs. They have been very helpful to me.
Yesterday, I went out and redid the braking with the ABS on. I achieved the exact same results. You seem dissatisfied with the maximum braking. Can we agree that in a stop from 18 mph, the transition time is a larger percentage of the stopping distance than from 25 mph? Am I correct in suggesting that .67 is a lower number than I'd calculate from a higher speed given the same efficiency in braking?
When summing forces on a motorcycle, we can consider it as if it's suspended from a balance point at the CG with the base of the balance below the ground.
I'm pretty sure I'm correct in stating that the rotation moment in the case where just front brake is applied = Ff*h. This is opposed by a decrease in the force pushing up on the rear tire and an increase in the force pushing down on the rear tire. up on the front tire.
Given that the maximum braking attainable from just the front tire is only .57, what does this say about the height of the CG compared to a bike where the maximum braking from the front tire is .7? Is it higher or lower?
|
Most Recent Posts
|
Activity History
|
Safety Tips
Motorcycle Braking Dynamics
Posted - 08/23/2009 : 7:18 PM
Administrator
