Lateral G's In Relation To Lean Angle And Speeds

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Hi everyone. I'm a new rider - 3 month but an experienced Spec E30 (Infineon / Thunderhill) driver and I absolutely love understanding the physics that control cars, and now motorcycles.

Looking all over the internet and forums for a simple question "how many lateral G's can a bike pull in a corner" I found all sorts of answers that were all different from each other.

I ended up plugging in some basic formulas into excel and compiled some graphs.

Here is what I learned:

1) Lean angle of 45 degrees = 1 lateral G. Regardless of tires, speed, or radius. 45 degrees will always produce 1G.

2) If you maintain a 45 degree lean angle and accelerate, your radius will increase. This is pretty obvious.

3) Lean angle vs lateral G's is not linear. For example - your first 10 degrees of lean angle will produce around 0.17 lateral G's. But the extra lateral G's produced by leaning from 40 to 50 degrees is 0.35. In other words - an extra 1 degree of lean when at 40 degrees will result in a much tighter radius change than lest say going from 20 to 21 degrees lean. I could you could also say that at higher lean angles - lean angle becomes more sensitive. The point of all this is that next time you are in a corner leaning 45 degrees, get your big fat head towards the inside just a couple more inches to increase the total system lean by 1 degree - it can make alot of difference in terms of increasing your lateral G's. And when you increase you lateral G's, your turn gets tighter - OR - you can go faster hahaha which would you choose?

Unfortunately, the data was pretty disappointing. Specifically, the exponential relationship between lean angle and lateral G's where it seems that only after 60 degrees lean, every little bit of extra lean starts to make a whole lot of difference in lateral G's. Up to around 45 degrees, it's almost linear. It just goes to show me the importance of cracking that 45 degree lean barrier and i'll be able to zip around these turns much faster. But again - a bit unfortunate that bikes can't lean to 60 or better yet - 70 degree lean.

PS - when talking about lean angle,we are obviously considering the entire system - bike + rider. If the bike alone is leaned 45 degrees, and the rider is vertical refusing to lean with the bike - you may have an overall system lean of 40 degrees.

The following formulas were used for getting lateral G's:

acceleration in m/s = velocity² / radius (all in m/s)

to convert to G's: accelleration in m/s² / 9.80m/s² = G's

The following formulas were used for lean angles:

Then you have to inverse tangent of tana and you get degrees of lean angle.

I hope this helps someone out there who thinks like I do. I usually have to understand the math and physics behind something before I'm willing to try it in real life.

Hope to see some of you at the school in 2013. I'll be attending in las vegas. I know Infineon very well, but wouldn't dare to try it on a bike - at least not yet.

Kind regards everyone.

Noam

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The following formulas were used for getting lateral G's:

acceleration in m/s = velocity² / radius (all in m/s)

to convert to G's: accelleration in m/s² / 9.80m/s² = G's

The following formulas were used for lean angles:

Then you have to inverse tangent of tana and you get degrees of lean angle.

This is why I left the engineering program in college

One of the school coaches posts here under the alias "tzrider". I think he has the math/physics background for this question so hopefully he'll spot this thread.

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I think he already answered his own question! He has made some good observations. In particular, finding that the amount of G force changes more dramatically at higher lean angles AND that rider position has a greater influence at higher lean angles, supports the idea that it will be nearly impossible to pin a specific number. Too much will depend on the rider and the particular bike setup and the conditions of the tire, track, etc. You'd probably just have to look at measurements from top racers and find a range of data.

I get interested in the physics side but I only find it useful up to a point - there are SO MANY variables (rider, suspension, tire compound, temperature, etc.) that the calculations quickly become overwhelmingly complex - or you end up oversimplifying and ignoring so many factors that the solutions are unrealistic and not useful. Data acquisition is so much simpler...

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Thanks for the replies!

Speaking of data acquisition - what is popular in the bike world?

I use traqmate for my racecar. I'm going to mount it on my motorcycle soon and see how it does?

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At 90 degrees of lean, you will get the best effect from staying in line with the machine. If you hang off, the bike will lean, which will not benefit you regarding maximum obtainable G forces. OTOH, if you want to alter your trajectory, it will be beneficial to shift your weight, but then you can overcome tyre traction. At 90 degrees of lean riding in a straight line, CoG doesn't matter as all the forces goes straight through the bike and through the tyres and onto the ground.

If leaned over at 45 degrees or more, since tyres have width, I would expect that you will want to sit as tall as possible for maximum cornering speed to raise the CoG. It's like holding a long, thin stick at one end; the further you lean it over from vertical, the heavier it becomes. If you have a short, thick stick of the same weight, my instincts tell me the changes in effort required will change less. Hence it makes less sense to me to hang low with the head near the inner handlebar when leaned over for instance 60 degrees than hanging off with torso fairly errect.

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Hi everyone. I'm a new rider - 3 month but an experienced Spec E30 (Infineon / Thunderhill) driver and I absolutely love understanding the physics that control cars, and now motorcycles.

Noam,

Welcome to the site.

I also love the physics behind moving things (dynamics).

The 1g Club - by Keith Code

http://www.motorcycl...aning_the_bike/

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Thanks cornering master!

Regarding tire width in a lean, I think you are 100% correct. About 2 weeks ago I drew this on my laptop:

It tells me that the higher your CG (the more you sit upright on your motorcycle) during a corner, the less lean angle you will need.

Hope you understand the drawing.

As shown in the red line with a low CG, the actual lean angle is not as steep as the perceived. This is bad. It means you are leaning 45 degrees on the tire, but your bike is cornering with a 40 degree lateral force.

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Very interesting topic indeed

I did well in physics in college so i can understand for the most part ~

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