Need some maths help, comparing human acceleration with a motorbike

Chat Forum

[closed]

Need some maths help, comparing human acceleration with a motorbike

19 posts & 11 voices | Started 1 year ago by brooess | Latest reply from HoratioHufnagel

Tags:

No tags yet.

brooess - Member

There's this girl I work with, semi-pro athlete, runs 60m in 8.38 secs. She also rides motorbikes, has a Suzuki GSXR 600 which does 0-60 in 3.21 secs.

What I'm trying to work out is how she gets to 60mph faster, on the bike, or on her own two feet. My maths ain't good enough to work out how long it would take the bike to get to travel 60 metres from a standing start. Speed=distance/time obviously isn't going to work because there's going to be constant acceleration over the measured period. Anyone know how I can work this out?

ta

Posted 1 year ago #
Junkyard - Member

she does not get to 60 mph on foot

60 mph = roughly 1600m per minute or 266 m per 10 seconds @ 60 mph

The acceleration would be difficult to work out as I very much doubt the acceleration is linear but if it is doing 60 mph by 3.21 secs it then has 5 secs @ 60 so 133 metres there alone.

Posted 1 year ago #
cynic-al - Member

25 years since me O levels...

IIRC v^2=u^2+ 1/2 * a * t

Where v = speed after acceleration, u = speed before, t = time of acceleration and a = acceleration.

Things is she's unlikely to be accelerating constantly all the way through her 60m EDIT and NO WAy is she hitting 60mph obviously (more like 20 IIRC)

Posted 1 year ago #
bassspine - Member

1)bike won't accelerate at a constant rate
2)she can't run at 60mph

Posted 1 year ago #
clubber - Member

s = ut + ½ at²

s is distance (60m)
u is starting speed (zero)
a = acceleration
t = time

so 60 = ½ a x 8.38²

so a = 60 x 2 / 8.38² = 1.71m/s/s

her acceleration is 1.71m/s per second

for the motor bike, 60mph = 96kph = 26.6m/s

so it's 26.6m/s / 3.21s = 8.3m/s per second

Of course, she never reaches 60mph though - her speed as she crosses 60m is 14.3m/s - 32mph ish though again, that's assuming constant accn.

Posted 1 year ago #
cynic-al - Member

Wow I forgot to LOL at teh fact someone could even think you can run faster than a 600cc sports motorbike!

Posted 1 year ago #
clubber - Member

Me too.

LOL!

Posted 1 year ago #
brooess - Member

Doh! I hereby nominate myself for STW numpty of the day award.

I meant 60m, not 60 mph! Her 'on foot' 60m time is actually 7.6, slightly faster.

Posted 1 year ago #
cynic-al - Member

So what was the question?

Posted 1 year ago #
brooess - Member

ok, question was: what's the quickest way for her to get to 60 metres from a standing start on foot or on the bike?

Take the point about the LOL - this is just an intellectual curiosity! I'm just kind of interested in how close the margin is

Posted 1 year ago #
clubber - Member

Well again, assuming constant acceleration then the bike is way quicker - it accellerates almost 5 times as fast as her on foot.

Posted 1 year ago #
stumpy01 - Member

She will accelerate pretty quickly to max speed (perhaps within 15m) and then the remaining time will be spent at that constant speed (almost).
Assuming she can run at 20mph (~9.1m/s) and it has taken her 15m to reach that speed, then she has 45m still to run at 9.1 m/s, meaning it'll take her 45/9.1 = 4.9secs to cover the constant speed section of the 60m. Add on a couple of secs to get out of the blocks & cover the initial 15m acceleration phase & that's now up to 6.9 secs.

Assumin the bikes acceleration is linear, it accelerates at 60mph/3.21s = 27.3m/s / 3.21 = 8.5m/s.
Initial speed is 0, so s=1/2at^2. Rearranging for t gives approx 3.75s to cover 60m.
It'll still be in 1st at 60mph (I think), so no need to account for any gear changes.

So, the bike is almost twice as quick.

Now show me where i've gone wrong!

Posted 1 year ago #
clubber - Member

The bike won't be linear though will it - early on, grip will be the limiting factor and then at some point, depending on the torque curve/gears/etc that will stop being an issue and the acceleration will increase.

Posted 1 year ago #
david_r - Member

Simple test. Get her to the start of the 60m course with her motorbike, but instead of sitting in it, she stands by the side of it, winds it open and then runs as fast as she can.

If she felt like she was pushing it all the way = shes a faster runner.

If she gets dragged and it all goes wrong = bikes faster.

Can you please video this as well.

Posted 1 year ago #
Trimix - Member

Actually, the limiting factor on the bike is more likely to be the rider. With a std sports tyre and a normal sports bike its pretty hard to spin the rear wheel. What normally happens is the front of the bike just goes skywards and you s4it yourself, close off the throttle, or jump off the back.

Posted 1 year ago #
Northwind - Member

"The bike won't be linear though will it - early on, grip will be the limiting facto"

Not grip, but flip- sportsbikes are fairly unstable (intentionally) which limits their launches.

Posted 1 year ago #
molgrips - Member

Compare her speed profile with that of the motorbike. She'll reach max speed before the bike has even got its power on the ground.

This has been done with cars IIRC and the athlete is only faster over about 5m or something.

Neither the bike's or the runner's accelerations are at all linear over such short distances (or even at all) so put your GCSE Physics away

Posted 1 year ago #
stumpy01 - Member

Yeah, correct. I am aware that neither of the accelerations will be linear but with the information given it's all pretty much a broad guess.

Unless anyone who pointed out that the accel. isn't linear/that grip will/won't be a factor etc. fancies gleaning the necessary info from that provided....I reckon it's about as good a stab as you are going to get.

In fact, the OP mentions that the runner covers the distance in 7.6s, maybe slightly faster so my estimate of 6.9s wasn't that far off.

Posted 1 year ago #
HoratioHufnagel - Member

i typed 'human acceleration" into google and ended up here http://en.wikipedia.org/wiki/John_Stapp
wow! this guy withstood 45g (equivalent of 1000-0 mph in 1 second) and an F1 driver deccelerated from 107mph in a space of 66cm!

sorry, went a bit OT there...

Posted 1 year ago #

RSS feed for this topic

Topic Closed

This topic has been closed to new replies.

Singletrack Mountain Bike Magazine

Chat Forum

Need some maths help, comparing human acceleration with a motorbike

Topic Closed

Don't miss…

Singletrack

Website & Forums

Exits