Lean angle vs G-force

[*caution*]

But alas you all still haven't got the joke, constant speed, angle with 0.5G!!!

Is the joke your trying to get at, that its constant speed, but its accelerating (0.5G)? because I figure hes implying constant speed perpindicular to the radius of the bend..... while of course the bike is also accelerating toward the centre of the bend (basic rotational mechanics) or else it wouldn't be turning.

enough for a friday anyway....

[Mikkel]

But alas you all still haven't got the joke, constant speed, angle with 0.5G!!!

I think it would be worthwhile to point out that while velocity is a vector (it has a magnitude AND a direction) - speed is just the magnitude of the velocity vector.

You can have acceleration change the direction of the velocity vector - but not the magnitude - thus maintaining a constant speed.

[McJim]

What a silly place to ask this question. You're troll aren't you?

I just go round corners and lean just enough not to fall off.I tend to leave my protractor at home.

[speedpro]

I've hopped off my bike mid-corner a few times. Alas I didn't think of carrying my protractor so I could measure what was happening. Some of it was pretty obvious though, the old sky,earth,sky,earth thing and once there was an "F5 Dave" in there somewhere as well.

[Cruisin' Craig]

O.K then. Take a look at the attached picture if you will.

The horizontal line at the bottom is the ground, and the diagonal line represents the bike at some angle of lean.

AC represents the downward acceleration of 1.0G, which is equal to the two component vectors CB and BA.

If you take a moment to check, you will see that x is equal to the angle of lean.

Now if you look at the first triangle: ABC, you can see that it has three angles. One is 90 degrees, one is x, and the other is 90-x degrees.

Look now at the smaller triangle BCD, and you will see that one angle is also 90 degrees, one is also x, and the other must therefore also be 90-x degrees. This means that ABC is exactly the same shape as BCD, just bigger.

This means that the ratio between AC and BC (the hypotenuse of each triangle) is equal to the ratio between BC and BD (the opposite of each triangle). Or in other words: AC/BC = BC/BD.

Multiply both sides by BC*BD and we get AC*BD = BC*BC

Note also that CD = 0.5G as this represents the centripetal acceleration.
This means that AC (also known as G) = 2*CD. Substitute this into the above equation and we get BC*BC = 2*CD*BD

Then we use pythagoras on the smaller triangle to get:
BC*BC=BD*BD+CD*CD

Or substituting BC*BC with the equation from two lines up , and you are left with:
BD*BD+CD*CD=2*CD*BD

which can be re-written: BD*BD - 2*CD*BD + CD*CD = 0

or Factorising: (BD-BC)*(BD-BC)=0

This shows that BD = CD, and if you look at the diagram this clearly means that x = 45 degrees.

The 26 or so degrees spoken of earlier was correctly calculated, but this is the angle of the total accelerative force, and is not the same as the angle of lean (as has already been said).

The angle of lean is 45 degrees.

[ital916]

Thats what I was saying, for 5khr, slow, tight turn, small radius to create 0.5G.

Can't say i've got my book on me, I remember we used engineering mechanics: dynamics, (meriam and kraige if i rememeber correctly)!! Vectors are king, who was that lecturer agian, simon B....someone i think, he had this slide he would put up "Only a fool doesn't draw a vector diagram!" haha

Haha gotta love the dynamics text book. Guess we will be wrapping our heads around this kind of problem this year in eng. ....I care..cos engineering is the "shizzle", especially when people do awesomely useless stuff, just cos they can. Like the Y2K.

[ital916]

O.K then. Take a look at the attached picture if you will.

The horizontal line at the bottom is the ground, and the diagonal line represents the bike at some angle of lean.

AC represents the downward acceleration of 1.0G, which is equal to the two component vectors CB and BA.

If you take a moment to check, you will see that x is equal to the angle of lean.

Now if you look at the first triangle: ABC, you can see that it has three angles. One is 90 degrees, one is x, and the other is 90-x degrees.

Look now at the smaller triangle BCD, and you will see that one angle is also 90 degrees, one is also x, and the other must therefore also be 90-x degrees. This means that ABC is exactly the same shape as BCD, just bigger.

This means that the ratio between AC and BC (the hypotenuse of each triangle) is equal to the ratio between BC and BD (the opposite of each triangle). Or in other words: AC/BC = BC/BD.

Multiply both sides by BC*BD and we get AC*BD = BC*BC

Note also that CD = 0.5G as this represents the centripetal acceleration.
This means that AC (also known as G) = 2*CD. Substitute this into the above equation and we get BC*BC = 2*CD*BD

Then we use pythagoras on the smaller triangle to get:
BC*BC=BD*BD+CD*CD

Or substituting BC*BC with the equation from two lines up , and you are left with:
BD*BD+CD*CD=2*CD*BD

which can be re-written: BD*BD - 2*CD*BD + CD*CD = 0

or Factorising: (BD-BC)*(BD-BC)=0

This shows that BD = CD, and if you look at the diagram this clearly means that x = 45 degrees.

The 26 or so degrees spoken of earlier was correctly calculated, but this is the angle of the total accelerative force, and is not the same as the angle of lean (as has already been said).

The angle of lean is 45 degrees.

I find with mathematics, if you try hard enough you can prove that something is something else using enough mathematical know how. A prim example is of a maths teacher proving 2 = 3. Gotta find it on google.

[DingoZ]

Get up cause it's so ..
Yes thinks it's : Great day for a ride
Go out and start the Bike
I'm gunna enjoy this ride, cause I learn something every time
Got that corner a little bit wrong
Got the Groove now
Fark I like this motorcycling stuff - why did I wait so long

The above stuff has got me all

.....Everyone and let's all enjoy the

[Cruisin' Craig]

I find with mathematics, if you try hard enough you can prove that something is something else using enough mathematical know how. A prim example is of a maths teacher proving 2 = 3. Gotta find it on google.

It won't be a real proof though. If you find it and post it, I'm willing to bet I can show where they cheated :-)

[ital916]

I'll try my darndest to find it. I wonder if we will build anything cool in the third year eng ..jet bike anyone lol

[Disco Dan]

Five pages and no G-spot... not even a G-string...

[Jantar]

O.K then. Take a look at the attached picture if you will.

The horizontal line at the bottom is the ground, and the diagonal line represents the bike at some angle of lean.

AC represents the downward acceleration of 1.0G, which is equal to the two component vectors CB and BA....

And that is where your analysis fails. AC is NOT the resultant, it is a component vector. CD is the other component, and AD (not drawn) is the resultant. Now try again.

[Cruisin' Craig]

And that is where your analysis fails. AC is NOT the resultant, it is a component vector. CD is the other component, and AD (not drawn) is the resultant. Now try again.

I have broken AC down into two vectors. Therefore those two vectors are the component vectors of AC, and AC is the resultant of those two vectors. Get it?

Now if you want to add two different vectors together to get a different resultant vector that's fine, but it doesn't affect the truth or otherwise of my argument.

[EnzoYug]

Does the corner tighten up just before you realise you've gone in too hot?
Is there loose gravel on the road?

I've run a few tests and found 90' to be about right - it depends if you're bouncing alongside or underneath the bike as it grinds away the plasticy bits.

[Jantar]

I have broken AC down into two vectors. Therefore those two vectors are the component vectors of AC, and AC is the resultant of those two vectors. Get it?

Now if you want to add two different vectors together to get a different resultant vector that's fine, but it doesn't affect the truth or otherwise of my argument.

AC is a vector. It has direction = towards the Earth's center, and it has magnitude = 1.0 G.

Your diagram gives AB at direction x as a component of AC, however it is the resultant of AC and is the hypotenuese. ACB is the right angle, not ABC.