Mathematics....

[t33zr]

Here one day i was going to do a big dropgap.

When i was on the top of the edge i was wondering if i where able to make it. (maybe i would die if not)

I bet everyone have been on top of something, preparing for a gap and not know if they would make it or not.

Then i suddenly got a idea..... is there any mathematical method to calculate if u are able to do a big drop gap?

Lets say i can gap 3m....thats maximum flat to flat....

If i am going to take a gap that is 4m long, and 1,5m high difference... (down)

Will i make it?

Is it posible to do some mathematics to figure it out?

[gilly]

In theory yes its possible but you would have to perform exactly the same movements when doing a drop gap to when you did that flat gap, and nobody does that! Its easy to work out that sort of thing with balls etc but with a person on a trials bike, with a constantly moving centre of gravity it would be very difficult.

My best advice is just go out there and try it and have fun, and if you don't want to, then don't do it! Come back to it when you're more confident that you'll make it

Edited July 24, 2008 by gilly

[TheChai]

Here one day i was going to do a big dropgap.

When i was on the top of the edge i was wondering if i where able to make it. (maybe i would die if not)

I bet everyone have been on top of something, preparing for a gap and not know if they would make it or not.

Then i suddenly got a idea..... is there any mathematical method to calculate if u are able to do a big drop gap?

Lets say i can gap 3m....thats maximum flat to flat....

If i am going to take a gap that is 4m long, and 1,5m high difference... (down)

Will i make it?

Is it posible to do some mathematics to figure it out?

work out by experiementing rather then maths.. u say u can jump 3 m flat to flat.. try andn do the same thing off a 1 meter hgih plateform and see where u land.. i think estimating u should be roughly 50 cm further.. when u get this u can ratio it out.. its much easier then measuring ur acceleration and stuff. which would need to be done if u wanna work it out purely by mathematics..

[ben_travis]

I would assume it is possible to make some sort of mathematical calculation so that you know how far you can make. however, things i think you would have to add into the calculation are as follows:

• distance you can gap flat to flat
• gravity
• height difference
• 'fresh-ness' of muscles
• wind resistance
• tyre pressure (will more or less pressure give you better gappage)
• total bike and body weight at exact moment of take off (would a lighter bike or body make it easier to gap further)

i think there is probably more. and ill probably get shot the f**k down by an engineer, however bring it on

[Joe_Elding]

If you can work out your initial velocity just as you leave the ground off of your hardest kick, then you can work out how long it would take you to do the horizonalt distance, and work out how long it would take you to do the vertical movement due to gravity, if the time it take to do the horizontal is shorter than the time it takes to fall you'll make it.

[PaRtZ]

I theorise, that as gravity is an accelerative force, your drop gap capabilities will DECREASE exponentially as you inital height increases.

You can work it out using basic projectile knowledge (all assuming you are constant etc as said above) and SUVAT equations too

v² = u² + 2as

[gilly]

I would assume it is possible to make some sort of mathematical calculation so that you know how far you can make. however, things i think you would have to add into the calculation are as follows:

• distance you can gap flat to flat
• gravity
• height difference
• 'fresh-ness' of muscles
• wind resistance
• tyre pressure (will more or less pressure give you better gappage)
• total bike and body weight at exact moment of take off (would a lighter bike or body make it easier to gap further)

i think there is probably more. and ill probably get shot the f**k down by an engineer, however bring it on

I'm doing Engineering and i pretty much agree with you there so don't worry! As i said above you'd need to take into account body movement during the gap ( like if you push the bike forward etc). Also i'm fairly sure that although muscle freshness needs to be taken into account, its impossible to measure!

I theorise, that as gravity is an accelerative force, your drop gap capabilities will DECREASE exponentially as you inital height increases.

You can work it out using basic projectile knowledge (all assuming you are constant etc as said above) and SUVAT equations too

v² = u² + 2as

Horizontal velocity is not related to vertical velocity. No matter how high you are, you will only ever go as far as you can physically kick away from the wall. So yes you're right, eventually you will reach a point where extra height won't help you any more, although i suspect that at this height doing a drop gap would be ridiculous anyway!

[bikeperson45]

This is too clever for me

[psycholist]

Look up ballistics calculations - anything flying through the air with only gravity acting on it will follow a parabolic path. The combined centre of gravity of you and the bike will follow a parabola as you fly through the air during a gap. The usual way to solve for distance is to solve for the time of flight in the vertical direction - initial vertical velocity component u, acceleration due to gravity, -g (Negative for coordinate system with vertical direction positive), time of flight t, and height change between takeoff and landing, s, using the equation: s = ut - 1/2 gt^2. The value of s will be negative if the landing is below the take off height, zero if they're level or positive if the landing is higher. Rearrange the equation to the standard quadratic form ax^2 + bx + c = 0 and solve using the quadratic solving formula to get the time of flight, t. To find the distance take the horizontal component of the take off velocity and multiply it by the time of flight - say 4 m/s * 0.5 s = 2 m...

The problem with this is it's hard to measure the initial take off velocity, the peak height of the parabola (Given it's the average of the centre of gravity of the bike and rider this is hard to measure even on video) or the flight time and one of these is needed (Along with the dimensions of the gap) to define the shape of the parabola. Flight time measured off a decent frame rate video is your best chance of getting data to put in to the equations...

Here's what NASA says about the whole subject: http://exploration.grc.nasa.gov/education/.../ballflght.html

[Tomm]

There are way too many assumptions to work it out. For example, at the precise moment you land a normal gap, your weight (well, your centre of mass) is rarely over the obstacle you land on, and it's also significantly lower than when you leave the lip. So even a flat gap couldn't be worked out using formulas like that. Too many assumptions would have to be made.

[Greetings]

This might start a whole new trend of riding. I can imagine a conversation like this:

-Hey guys, according to my PDA I can gap from this wall to that one.

-Cool, you're a great rider. Now let's go and find some new gaps and see if you can do them.

[Barbara Logan-Price]

Some people really do think into trials too much :|

[Jamie_Neal]

The other issue when considering this is that the rider usually moves the bike around quite a lot when doing a flat gap and cannot really be considered as a ball (or whatever is used in these examples).

When drop gapping, the rider probably does move in more of a parabolic shape although they still do move the bike a fair amount on the take offs of large drop gaps.

Would make an interesting study but its too long since I've had to do this sort of maths.

[psycholist]

Once you have the flight time you should be able to solve for the parabolic path. If you're to land balanced, the centre of gravity of the bike + rider must end up above the contact patch of the tyre. If there's a change in the height of the combined centre of gravity this should be added to the gap height change in the equations, but I don't think it needs to be to affect the usefulness of these equations as a guideline. Also given that most people extend the bike into the landing, pretty much everyone will gap further than their initial takeoff velocity would suggest (But that's a fixed offset and won't be affected too badly by the length of the gap unless your technique changes drastically depending on the gap you're doing).

Once the bike and rider are in the air gravity is the only force acting on them (Gyroscopic forces from the wheels spinning will play a very small part if there's spin involved in the hop, but can safely be ignored at trials speeds), just because it doesn't look like an obvious parabola doesn't mean that's not what's happening though. If the centre of gravity of the bike and the centre of gravity of the rider are averaged you'll find the average following a perfect parabola every time (Unless outside forces such as wind are also acting on the system).

Edited July 24, 2008 by psycholist

[Tomm]

If you're to land balanced, the centre of gravity of the bike + rider must end up above the contact patch of the tyre.

In reality that doesn't happen at all though. At the instant of touching your tyre onto the wall you're gapping to, your weight won't be above the wall. Your forwards momentum, and shifting your weight (shagging the bike) will keep you moving forward so you can reach a balance point, but that occurs afterwards. It's very complicated, because when your wheel contacts the wall, you have something to push against.

[t33zr]

This might start a whole new trend of riding. I can imagine a conversation like this:

-Hey guys, according to my PDA I can gap from this wall to that one.

-Cool, you're a great rider. Now let's go and find some new gaps and see if you can do them.

Haha... lol...

The reason i want to know this, is its often hard to see if its posible or not when things starts to go high and long...

Then it will be easy to measure the height and length and tell if my body are able to do it...

This is only the theoretic part... the mental part will still hold me back, even if the calculations say i can do it...

[psycholist]

In reality that doesn't happen at all though. At the instant of touching your tyre onto the wall you're gapping to, your weight won't be above the wall. Your forwards momentum, and shifting your weight (shagging the bike) will keep you moving forward so you can reach a balance point, but that occurs afterwards. It's very complicated, because when your wheel contacts the wall, you have something to push against.

Stretching the bike out to a landing increases your gapping distance over the theoretical distance suggested by your takeoff velocity. This will add to the gap length, but by the same amount for each gap. Because the bike and rider are separate masses which can be moved relative to each other, a more complex model (Based on exactly the same equations as before) is needed if you want to account for movement between the bike and rider. Regarding the difference in gapping range where there's a drop from the takeoff to landing all that extra calculation will tell you nothing new though as for almost all of the flight the bike and rider still follow a parabolic path.

[Nick Manning]

In all fairness, when a rider gets to a certain standard, or is trying a particular technique, they almost always think about mathematical possibilites. If your tapping a wall, you slowly work out a position (angle) that your bike needs to be at to be able to get up the wall. Whether you physically think about what the degree of the angle is when you tap or not. A rider will still be thinking mathematically when doing that technique.

Same with gaps, as said by other's. You probably can work out a mathematical method to work out whether a gap could be made or not, ut for the time and hassle it would course.

In all, I agree with Gilly.

It is just easier to stick to you limits, and push them only if you feel happy and comfortable to and not to try something under peer pressure.

After awhile, you get an eye for what your limits are. So whether it's a gap, sidehop, tap, hook, or any other technique. You'll be able to take one look at the obstacle, and know whether you'll be able to do it with ease, or with effort, or not at all.

[SuperDeathMonkey]

NERD!!!!

[Greetings]

The reason i want to know this, is its often hard to see if its posible or not when things starts to go high and long...

Then it will be easy to measure the height and length and tell if my body are able to do it...

This is only the theoretic part... the mental part will still hold me back, even if the calculations say i can do it...

I'm not having a go at you mate, just thought there was a funny side do it as well

[Tomm]

Stretching the bike out to a landing increases your gapping distance over the theoretical distance suggested by your takeoff velocity. This will add to the gap length, but by the same amount for each gap.

I don't think that's the case - You're over-simplifying it. If a rider lands a 9ft gap, he will be moving much faster than if he does a 2 ft gap, and will have more momentum to carry his weight forwards. If you see someone land a huge gap, their arse will be way back over the back wheel, but they can still regain their balance.

Too many assumptions?

[psycholist]

That's still only a slight modification to the overall gap distance though - weight shifting on the bike including pushing the bike forward will add a foot or two onto a gap, but regardless of what happens at the landing, the flight remains parabolic...

[PaRtZ]

Horizontal velocity is not related to vertical velocity. No matter how high you are, you will only ever go as far as you can physically kick away from the wall. So yes you're right, eventually you will reach a point where extra height won't help you any more, although i suspect that at this height doing a drop gap would be ridiculous anyway!

Sure about that? What about when vertical velocity = 0? (ie you hit the ground or are just taking off) does that effect horizontal velocity? yes, yes it does.

I never said that there is a point where height doesn't matter as well. As there is no horizontal deceleration, you will always be able to travel at the same velocity. It just so happens that as you fall more and more, your vertical velocity increases (due to gravity) and in comparison, makes your horizontal velocity look minimal.

[Luke Rainbird]

Try adding in the size of one's testes into the equation, multiply by the coefficient of howgoodadayyou'rehaving and divide by the attempts so far. Raise to the reciprocal of the number of punctures in the past week to the crank-length root, and then realise it's a silly idea and just have a bash if you think you can

[gilly]

Sure about that? What about when vertical velocity = 0? (ie you hit the ground or are just taking off) does that effect horizontal velocity? yes, yes it does.

I never said that there is a point where height doesn't matter as well. As there is no horizontal deceleration, you will always be able to travel at the same velocity. It just so happens that as you fall more and more, your vertical velocity increases (due to gravity) and in comparison, makes your horizontal velocity look minimal.

Yes i am sure. At the points your talking about the object is touching the ground which brings friction into play and alters the speed. Horizontal velocity is not changed or made bigger just because you happen to be falling at the same time, you will still be travelling across the ground horizontally at the same speed.

It's also impossible to keep going through the air horizontally at the same speed, as every gap you do is affected by air resistance. Eventually you will reach the point where you stop moving horizontally, and just keep falling but not going forwards. But as i said earlier, the height you would need for this to happen would be ridiculous!

That's still only a slight modification to the overall gap distance though - weight shifting on the bike including pushing the bike forward will add a foot or two onto a gap, but regardless of what happens at the landing, the flight remains parabolic...

Your right, the flight path of the combined centre of mass of the rider and bike will be parabolic as neither is affected by any external forces other than gravity (except air resistance which always complicates everything). However it would still be very hard to use this work anything out because your really interested in where the tyre is, not the combined centre of mass.....Then of course you need to think about where the centre of mass is in relation to the tyre once you've landed, and how fast you're going, to see if you'll be able to hold the gap or fall off backwards.

There are really too many assumptions to work it all out seriously.

Edited July 24, 2008 by gilly