Maximum Radius for Wall of Death

[mgkii]

Hi - Can anyone help me out with a question. The answer seems obvious, but maybe so obvious that I'm jumping to wrong conclusions!

Just been reading Guy Martin's book "When your dead, your dead" (good read by the way) and one of his stories is about breaking the world speed record for a wall of death. I've looked at the math around wall of death mechanics and it all seems pretty straight forward, but here's what's puzzling me.

1. There's plenty of forces to worry about when riding the wall of death, but the one that appears to limit your speed is the G Force acting on the rider/bike as a result of centripetal force when you run at a constant "speed" - but constant acceleration in velocity terms around the inside of the wall.

2. The smaller the radius of the wall of death, the higher the G Force acting on the rider and bike, so if you want to go faster, you build bigger.

3. I've read a number of different sources to try and understand the basics of the forces acting on ride/bike and the diagrams all seem to ignore radius - or rather they remove the complexity of centripetal force due to acceleration around the circle, but look at the bike as the frame of reference using the (fake) centrifugal force. The upshot seems to be that as long as you generate sufficient "centrifugal force" by going fast enough, then you're going to stay on the wall.

4. There's also a torque factor involved. Because the force of gravity acting downwards on the bike is from the centre of mass, and the force of friction on the wall from the tyres is acting at a distance from the centre of mass, then you need to lean the bike "up" the wall to stop it falling over. A coupe of sites have a graph that show that the slower the speed, the more you have to lean - so the faster you go the more you can ignore this torque effect.

5. It would therefore seem that in principle there's no maximum limit to the size of a wall of death - as long as you can get sufficient speed, you can ride an ever larger wall. And the larger the diameter the lower the G Force acting on the rider for any given speed. So obvious, but presumably so wrong!

6. Case for the prosecution: Before Guy Martin kick starts his bike, they get someone that actually understands the math involved (!) and determine that the fastest Guy is going to get up to is 80 mph on a wall of a particular radius (around 150 feet) and, that at this speed/radius he will be subject to 6G (which is where he puts his limit of "almost blacking out"!)

So - my question is what am I missing? Given that Guy is after a world record and has access to bikes that can top 200mph; why build a wall that limits him to 80mph? What is the limiting factor in the radius of wall of death?

Thanks all!
Matt

 

[Hornbein]

What is the limiting factor in the radius of wall of death?

Thanks all!
Matt

The money to build it?

 

[mgkii]

I have to say that did occur to me . The only reason I didn't see the cost as the limiting factor in this case is that the book made quite a point about seeming to work back from a speed and G-Force and coming up with size. Guy Martin is such a straight-talking no-BS kind of guy, I think if it was the other way around he would have said that they built a wall to a budget and then he went balls out around it until he passed out!

However - I'm happy to be disabused of this idea! Are you actually telling me that there is no limit to the radius, or just suggesting that there may have been a more practical cost limit at play?

 

[mgkii]

Maybe I've confused the question with the book references :-)

Can anyone enlighten me on the basic question: Is there a maximum radius for a wall of death** or is it as simple as "the bigger the radius, the faster you need to go"?

** that doesn't send some fundamental variable to a level that would invalidate it as being a wall of death - for example, g-forces or a lean angle increasing as radius increases

Thanks

 

[minilandrover]

hi as seen in the film g is equal to speed squared ( in kph) over 25 x diameter (in meters)
so guy is doing say 100 kph in a circle that's 100 m diameter so g equals 100 squared (10000) over 25 x 100 (2500) equals 4g
to do 200 kph and only pull 4 g you need a diameter of 400 meters . so no disrespect to Guy as he pulled more g than most people could stand.
If you build me a drum of 400 meters diameter, and give me a bike that will do 200 kph i will have a go at breaking the record ! all it takes is money...

 

[minilandrover]

earth has a dia of 12742 kms that's 12742000 meters and rotates at a surface speed at the equator of 1670 kph giving a g force of 0.00875 G so a man that weights 100 kgs on a set of scales at the north pole would weigh 100.875 kgs at the equator on the same set of scales, although his mass would remain unchanged !

 

[minilandrover]

sorry i forgot to subtract he would weigh 99.125 kgs at the equator !

 

[mgkii]

I'm so miffed I missed the TV show, having read his book that was one I was looking forward to!

Did they talk about the "lean angle" on the show when they were doing their sums on the size of the wall? As noted above:

4. There's also a torque factor involved. Because the force of gravity acting downwards on the bike is from the centre of mass, and the force of friction on the wall from the tyres is acting at a distance from the centre of mass, then you need to lean the bike "up" the wall to stop it falling over. A coupe of sites have a graph that show that the slower the speed, the more you have to lean - so the faster you go the more you can ignore this torque effect.

And if they didn't talk about it, did you see anything crazy on the film? I assume Guy had a camera on him or on his bike; from his ride perspective was he riding "on the flat" or did he look like he was leaning into a hard corner?

Thanks

 

[mfb]

The ultimate limit is just given by the size of Earth and the tolerance to g-forces. The size of Earth doesn't matter - even for the fastest aircrafts it is a small effect, and motorbikes are slower than aircrafts^{[citation needed]}. So money, motor bike speed and maybe risk aversion are the limit.

 

[minilandrover]

Yes I also missed half the show, i had promised to let my daughter see something on the other channel and didn't realize it was a two hour show... in the first hour we got the build up to the breaking the existing record, at some 60 kph or so but according to other sources he went on to set a super high record of 78.15 mph that's just over 125 kph ! and pulling over 6.32 G
Yes of course you have to lean the bike upward slightly as there is still 1 G pulling downwards to overcome, the centre of mass will be down the vertical line of Guy and the bike and the tyre. when it's at any G force , otherwise the bike would be climbing up the wall or falling downward, effectively in a turn, as you would lean a bike to take a turn on the flat!
The biggest problem of doing this record is that it's not like a drag-race..it takes time to get up the wall, and start to accelerate to a speed where you are set up to go for the MAX, during this setup you are pulling 3 or 4 G and leaning the bike upward, then by gunning it up to the point where you start to go blind and black out..you have to set in your mind to go past that point for a few seconds and still have the mind control to shut off the gas and really start to slow down..
The easy part is that a motorcycle is very stable the faster it goes, ( up to a point but well in excess of 300 mph ) but you are also fighting the G force trying to crush you against the tank of the bike..and this is where you can induce wobble and crash! there is also the G forces affecting the components of the bike it's self, compressing the suspension, the massive load on the tyres, the force trying to rip the engine apart and not least the battery acid that already has a high density of 1.8 kg per litre it now weights 11.3 kgs per litre, trying to split open the battery case. Anything that gives way on the bike and suddenly changes the centre of mass or even the weight of the machine if it falls off will upset the balance and start a wobble, not to mention that in a few seconds you will be running it over as you go around again...if all that is done safely you still have to recover from the blackout and not crash. Evil Kenivel jumping a few buses was peanuts compared to Guy's challenge.. but that's GUY MARTIN for you, he's one of the best bikers and sportsmen ever...I would be very humbled to shake his hand...

 

[minilandrover]

The ultimate limit is just given by the size of Earth and the tolerance to g-forces. The size of Earth doesn't matter - even for the fastest aircrafts it is a small effect, and motorbikes are slower than aircrafts^{[citation needed]}. So money, motor bike speed and maybe risk aversion are the limit.

There is a limit , the bigger the diameter the "wall of death" the faster you can or have to go to still stick to the wall. As I offered to have a go if someone puts up the cash...i don't think I could even stand 4 g's for any length of time due to my health conditions.

QUOTE..If you build me a drum of 400 meters diameter, and give me a bike that will do 200 kph i will have a go at breaking the record ! all it takes is money...

The problem is that with a 1 km drum you could do 400 kph and pull 6.4G but that would be the fastest bike ever, you would need a G suit, and a lot of high G time,,,you would basically be doing a tight turn as in a fighter jet...a 400 meter drum you can do 200 kph at 4 G's that's more realisable, and I am sure now the gloves are off that would be the next attempt if guy wanted to go even faster...but then it get's silly, the speed of the bike has to be so high to still stick to the wall and the diameter gets ridiculous...do the maths ! you just can't stay at 4 g for too long and 6+ g is down to seconds, the actual limit is going to be limited by the time to acquire the g's, the maximum G's, and the top speed of the bike...none of these limits is that far from what Guy has achieved..so it's likely to be a record that will never be broken by much if ever anyone with bigger kahoonies than Guy can be found ! . I am assuming there is a minimum lean angle for the rules of the record (eg 90deg to the vertical -+ 10 deg) or I could just ride in the desert at 200 kph in a big circle and claim a record !
AGAIN HAT'S OFF TO GUY MARTIN

 

[mfb]

There is a limit , the bigger the diameter the "wall of death" the faster you can or have to go to still stick to the wall.

Going faster was the whole point of the thread.
With higher speeds (which already means we are discussing a new record), the time to accelerate could become an issue, but you can cancel that with an even larger radius (if necessary) to keep the g-forces at an acceptable level. If you have enough money, of course, but we are discussing the physics.
A vertical wall can be rode at g-levels that trained humans can tolerate for basically infinite time (e.g. 2-3g), even if they would be standing. A motor bike rider is not standing.

 

[minilandrover]

Going faster was the whole point of the thread.
With higher speeds (which already means we are discussing a new record), the time to accelerate could become an issue, but you can cancel that with an even larger radius (if necessary) to keep the g-forces at an acceptable level. If you have enough money, of course, but we are discussing the physics.
A vertical wall can be rode at g-levels that trained humans can tolerate for basically infinite time (e.g. 2-3g), even if they would be standing. A motor bike rider is not standing.

my statement
quote "but then it get's silly, the speed of the bike has to be so high to still stick to the wall and the diameter gets ridiculous...do the maths !"

you didnt' do the maths did you ...i have just explained why this is why even going to a 1 km dia drum or wall the conditions de-pass human levels and who's standing ??
the optimum would be somewhere in the 200-300 kph region pulling 4-6 g in a diameter of 400 meters...
so do the maths ! take some sample theoretical speed (remember this is for a motorcycle) then take a diameter of you choice, and a human with his ability to withstand high g for the time it would take to get up to that theoretical speed and stop again, and the logistics of time acceleration duration, of the run...
so do the maths !

 

[mfb]

you didnt' do the maths did you

I did. Every speed is possible, as long as the motorbike allows it and the wall has a suitable radius. There is no optimal speed for a speed record.

 

[Jimbo54321]

Hi Guys, looking at the math for Guy Martin's wall of death.
g = kph2 / (25xd) 78.15 mph (125.77 kph)2 / (25x120) = 5.27 g fair enough.
In the show they showed Patch McGillicutty claim he done 71 mph and then used an equation of rev/s and the diameter of (9m) and said actually done 48mph
Using g = kph2 / (25xd) 48 mph (77.24 kph)2 / (25x9) = 26.51 g or dead as I'd call it.
If 6g is a reasonable max Transpose for kph = (The square root of) 6 x 25 x 9 = 36.74 kph or 22.8 mpg is more realistic of Patch's speed.
Ok 71 mph (cough cough) 71mph (114.263 kph)2 / (25x9) = 58.02 g
According to the mathematics in show only, are my maths right? and is Patch a liar liar with his pants on fire ?

 

[minilandrover]

Hi Guys, looking at the math for Guy Martin's wall of death.
g = kph2 / (25xd) 78.15 mph (125.77 kph)2 / (25x120) = 5.27 g fair enough.
In the show they showed Patch McGillicutty claim he done 71 mph and then used an equation of rev/s and the diameter of (9m) and said actually done 48mph
Using g = kph2 / (25xd) 48 mph (77.24 kph)2 / (25x9) = 26.51 g or dead as I'd call it.
If 6g is a reasonable max Transpose for kph = (The square root of) 6 x 25 x 9 = 36.74 kph or 22.8 mpg is more realistic of Patch's speed.
Ok 71 mph (cough cough) 71mph (114.263 kph)2 / (25x9) = 58.02 g
According to the mathematics in show only, are my maths right? and is Patch a liar liar with his pants on fire ?

YES Patch was a liar and so is someone who says they "have done the maths" ! come on
Do the maths take an example of a 5000 diameter drum or wall of death ( that's a 5 kilometre diameter wall of death..) the fastest bike say 400 kph ! that's 248 miles per hour, the g force resulting from going around would be 1.29 G yes only 1.29 G so he would fall off the wall, so go faster ! ok try 500 kph that's 310 miles per hour the G force is 2 G he would be leaning at 45 deg, still not enough
so go faster still , see where this is going ? by doing the maths !

Lets get really silly, let's say a tripple turbocharged nitro burning motorcycle, and 800 kph ! that's close to 500 mph and would get 5.2G ok that's about right to have the required angle to be reasonably close to 80deg to the vertical ! But to be traveling at 800 kph you would need a run up of 3 or four minutes and your blood would have drained into your boots well before, and you have to stay conscious during the slow down from 800 kph ! and let's face it no one is going to be able to build a 800 kph motorcycle without using rockets, parachutes and the rider would have to be genitally engineered with a bulls heart ! and a non resonating drum that's 5 km's diameter would have to be carved from rock to stop any induced vibration..

So let's not get silly...The maths actually do tell you that this is not feasible ! So there is an optimal maximum speed possible ! maths tells you that !

I would suggest that my first thought of a diameter of 500 meters and a shot at 200 kph 3.2 G to 250 kph at 5 G would me the maximum humanly possible !

But then I did the maths...and I am also a bike rider ! I have ridden a bike like Guys no fairing and at 200 kph, that' s starting to rip you from the handlebars and at 1G try doing 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800 kph each time you double the speed the wind resistance gets quadrupled ! so that ripping force at 200 kph of 20 kgs ( wind resistance to the exposed body and helmet ) at 800 kph would be like 320 kgs pulling you off the bike backwards.
Plus you have the downward (relative to the rider) force of 4 or 5 G's and all the forces applied to different parts of the motorcycle !t I rest my case ! impossible !

So please use a calculator and come up with some real figures if you think different !

I don't wish to annoy or offend but i get annoyed when I am told "I did the maths", when very obviously you didn't.

 

[mfb]

I rest my case ! impossible !

Based on a few numbers you made up?
"It is impossible to walk 1 kilometer. Try to move by 1 kilometer in a single second: it does not work! Try to walk one kilometer in two seconds: it still does not work! Therefore it has to be impossible to walk 1 kilometer."

You have an 800 km/h rocket motor bike? Fine. Build a 1700 m radius wall of death. The acceleration is now a reasonable 3 g, the leaning angle is about 20 degrees. As the rider is not standing upright on the bike, 3 g is tolerable for minutes, with training probably for at least an hour. The rider does not even have to pass out at all.

For every motor bike speed you can manage, there is a radius where the acceleration is 3 g and the leaning angle is 20 degrees (those are directly related). There is no fundamental limit below orbital speeds - just motor bike speed, available money, and risk for the rider.

 

[Jimbo54321]

.

 

[mfb]

I have no idea about the show - does the 9 meter diameter value come from there?
At that level, the difference between wall radius and center of mass radius of the rider becomes relevant - the person will have the same angular velocity, but a smaller radius, which reduces g-forces. Not sufficient to reduce 27 or even 58 g to a realistic level, but still relevant.

 

[minilandrover]

quote Let's get really silly, let's say a tripple turbocharged nitro burning motorcycle, and 800 kph !

as i said let's get silly, i meant in figures not your response ! and i walk a mile every day so does my dog we ain't dead yet
and you can't have a 800 kph motorcycle! it would have to be a rocket sled! perhaps if you had watched the show you would be better informed...

 

[MikeGomez]

as i said let's get silly, i meant in figures not your response ! and i walk a mile every day so does my dog we ain't dead yet
and you can't have a 800 kph motorcycle! it would have to be a rocket sled! perhaps if you had watched the show you would be better informed...

I thought a Physics Forum would be intelligent, my mistake !

Oh the irony.

 

[mfb]

and i walk a mile every day

I followed exactly your logic to show the "impossibility" to do so. As a corollary, your logic is flawed.

It does not matter how fast your motorcycle can go - there is a suitable wall of death radius for it. That is the point of the calculation. The upper limit is just the motor cycle speed, independent of its specific value.

 

[minilandrover]

watch the program now:: its on tv now
watch the show on now

 

[mfb]

Not in my country. If there would be relevant information, you could write it down here.

 

[minilandrover]

I dare say it will eventually end up on You tube so I would take a look from time to time..
The point you are missing is that the bigger the circle, the higher the speed required to generate the required G force, yes ? but the limit is the ability to make a bike and drum and actually ride the drum, the physical limit of the bike, (power) and the rider. Guy could only take 6 G for a matter of a few seconds, and with a small enough drum that he did a circuit in a few seconds accelerating up from 50 mph to 70 mph but to accelerate from 100 to 200 mph takes so much longer so you are having to take high G forces for longer...it's no good just looking at a figure that gives an instant force and speed, it takes time to get up to speed and back. When you get to see the actual record being broken,then you will start to realize that there is a lot more involved than just calculating the terminal speed and G force. So take a drum of 80 meters diameter, on paper that's done in a stroke, in reality it takes 3 weeks to build. You can't have a motor cycle doing 400 kph in an instant, it takes a build up of speed and that takes time...to get to running speed of 50 mph it took Guy three build up's and over two minutes, then to get up to 70 mph it took him longer as he had to build up the speed to a point that stresses the body, then go for a burst of speed from 50 to 70 before he blacked out..if the circle is kilometre in diameter then to do a lap at 100kph (less than 70 mph) will take 113 seconds and we know that you would be dead at 6G if you tried that. you cannot take 6G for nearly two minutes and ride a motorcycle at 100 kph without crashing...and you have to get up to 100kph and stop again so the g forces above 4G would last for at least 4 minutes with a peak at 6G for 113 secs to do the 31415 meters lap.!
As I said the probable limit is about 200 kph and a drum of 400 meters diameter. and no one is going to beat that ever, yet alone be daft enough to try...and I am sticking to that ! and you won't prove me wrong ..draw the curves, showing acceleration peak and deceleration and work out the time at any given G force and add up the time above 4G. then try and find pilot that can take 4G for five minutes and a peak of 6G for two minutes...

 

[mfb]

The point you are missing is that the bigger the circle, the higher the speed required to generate the required G force, yes ?

I am not missing that point, I calculated the relationship long ago.

but the limit is the ability to make a bike and drum and actually ride the drum, the physical limit of the bike, (power) and the rider.

The only limit is the speed of the bike, if the drum is built according to the planned top speed. The g-force can be set to 3 (by choosing the radius), which is tolerable for way longer than necessary to accelerate. There is no need to go to 6 g at all.
During the acceleration process, the rider will be on a non-vertical part, adapted to have a reasonable leaning angle at every speed, and a g-force below 3.

So take a drum of 80 meters diameter, on paper that's done in a stroke, in reality it takes 3 weeks to build.

So what, we don't have to break the record tomorrow. And as I said more than once, this is a physics discussion, money is not really relevant. A better record is more expensive - so what?

and you won't prove me wrong ..draw the curves, showing acceleration peak and deceleration and work out the time at any given G force and add up the time above 4G.

There is no time over 4 g at all. You can have that if you want, but it is not necessary.

 

[minilandrover]

so give me an example of your biggest diameter circle then. and let's assume the top speed of any motorcycle is 300 kph

 

[Jimbo54321]

Quote: hi as seen in the film g is equal to speed squared ( in kph) over 25 x diameter (in meters)

No they didn't.

Quote: but that's GUY MARTIN for you, he's one of the best bikers and sportsmen ever...I would be very humbled to shake his hand...

Man Crush ?

 

[Jimbo54321]

I have redone my math as I knew I was wrong and didn't know why. Hence I was asking if my mathematics was correct. Here are my workings out.

Patch McGillicutty’s wall of death = 9m diameter

1•3 seconds per revolution (according to footage)

In the show they stated that Patch achieved 48 mph, but my mathematics (using the one in the show) state that he would be pulling:

Assume 6 g's as a sensible max, transpose for max speed on a 9m diameter wall

Assume 9 g's as a max as Patch was wearing a G-suit and is a healthy fighter pilot.

Patch’s claim of 71mph.

Guy Martins wall was 37•5m in diameter

He attained 78•15 mph

Now, can somebody who doesn't live in the wardrobe that leads to Narnia confirm that what I have done is correct. If not can you please show the math, and not start by saying a 50,000km wall with a bike that can attain half the speed of light. I would appreciate it.Before you judge a man, walk a mile in his shoes.
After that, who cares?
He’s a mile away and you’ve got his shoes.

Billy Connolly

 

[mfb]

so give me an example of your biggest diameter circle then. and let's assume the top speed of any motorcycle is 300 kph

That is 83.3 m/s, to get 3 g we need a radius of$$r=\frac{v^2}{3g}=231m$$
If you want a different speed or acceleration just plug it into the formula.
We get a small correction from gravity, but that increased 3 g just to $\sqrt{(3g)^2+(1g)^2} \approx 3.1g$, so the effect here is negligible.

 

[Doc Al]

see you can work it out, although you got the wrong G force, Just don't go asking for a job at nasa

You might want to crack back the attitude. You're embarrassing yourself.

 

[Jimbo54321]

Quote: 187.5 mph squared over 3 equals 5468.75

I think your math is wrong, please feel free to correct me if my numbers don't add up.

Quote: 187.5 mph squared equals 35156.25 divided by your 231 meters ! will be 35156.25 over 25 x 231 this equals 6.087 G not 3 g !
who taught you maths ?
mfb stated the radius was 231m

Radius is half the diameter, is it not?

If 300 kph = 186.411 mph then the G forces would be;

Which brings us back to what mfb started with, 3 G's or be it a couple of decimal places out. Hehe,

Hi mfb, can you expand on your formula please, I'm trying to learn this for fun and I'm not particularly good at math.

I can see part of your workings out with regards to velocity which is measured in m/s:

Using your formula I found:

But when I bash these numbers into the abacus, I get:

What have I done wrong?

 

[Doc Al]

Using your formula I found:

The acceleration is 3g, not 3. (g = 9.8 m/s^2)

 

[Jimbo54321]

Hi Doc, I thought that was the case but when I used (rightly or wrongly) 83•3333² / (3 x 9•81) I got 235•964m
Which isn't what mfb got (231m), so I assumed I had done it wrong.

 

[Doc Al]

Hi Doc, I thought that was the case but when I used (rightly or wrongly) 83•3333² / (3 x 9•81) I got 235•964m
Which isn't what mfb got (231m), so I assumed I had done it wrong.

Close enough. The method is correct.