M25 Lap - difference in distance clockwise vs anticlockwise.

[mrmr96]

Here's one for you:

I had a couple of places to visit yesterday and ended up driving around the M25 and did a whole clockwise lap in the end. Towards the final stint I realised that if I had gone anti clockwise then my lap would have been shorter!

So then I started wondering: How much shorter is an anticlockwise lap versus a clockwise lap?

I have managed to get the answer and no doubt a lot of you will too.

So, anyone care to venture a guess?

[Flanders.]

Won't it be Anti-clock wise, as its a sligtly tighter turn.

[Podie]

Half a mile difference between inside lanes, IIRC

ETA - although technically you can't do a full lap on the M25, as the Dartford Crossing is not Motorway...

Edited by Podie on Thursday 14th May 16:30

[mrmr96]

Flanders. said:

Won't it be Anti-clock wise, as its a sligtly tighter turn.

You're right, anticlockwise is indeed shorter. The question is 'by how much?'.

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

[-DeaDLocK-]

Shame the M25's clockwise lanes aren't banked through the corners, a la Ehra-Lessien.

[Podie]

mrmr96 said:

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

I spent 6 months doing it each direction, each day...

[mat205125]

Podie said:

Half a mile difference between inside lanes, IIRC

How much will that shave off of my lap time?

[mrmr96]

Podie said:

mrmr96 said:

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

I spent 6 months doing it each direction, each day...

As I said, not a bad guess, but it's not right.

[Podie]

mrmr96 said:

Podie said:

mrmr96 said:

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

I spent 6 months doing it each direction, each day...

As I said, not a bad guess, but it's not right.

Not right on your vehicle.

I ran a data logging vehicle... if you want to get proper geeky, the length of the lanes varies as well due to slightly different incline rates...

[-DeaDLocK-]

Hmmm... but the tunnel and bridge are not technically the M25.

Since you're being anal...

[mrmr96]

Podie said:

mrmr96 said:

Podie said:

mrmr96 said:

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

I spent 6 months doing it each direction, each day...

As I said, not a bad guess, but it's not right.

Not right on your vehicle.

I ran a data logging vehicle... if you want to get proper geeky, the length of the lanes varies as well due to slightly different incline rates...

I didn't clock it. I worked it out.

I didn't take account of the bridge/tunnel or the incline rates. I do like that incline rates point. (Where's the paperbag smilie.)

[Podie]

-DeaDLocK- said:

Hmmm... but the tunnel and bridge are not technically the M25.

Since you're being anal...

See my first post, edited before you posted.

[Podie]

mrmr96 said:

Podie said:

mrmr96 said:

Podie said:

mrmr96 said:

Podie said:

Half a mile difference between inside lanes, IIRC

Not bad.

Anyone else got a guess?

I spent 6 months doing it each direction, each day...

As I said, not a bad guess, but it's not right.

Not right on your vehicle.

I ran a data logging vehicle... if you want to get proper geeky, the length of the lanes varies as well due to slightly different incline rates...

I didn't clock it. I worked it out.

I didn't take account of the bridge/tunnel or the incline rates. I do like that incline rates point. (Where's the paperbag smilie.)

C'mon then, what did you get..?

[-DeaDLocK-]

If you worked it out and are claiming that as being more accurate than Podie's datalogged measurements, let's see your calculations.

I expect it take into account every possible variable.

[youngsyr]

Googlemaps is no help, says 118 miles for both, but saying the circumference of the nearside lane clockwise is 118 miles and each lane is 3 metres wide and same again for the dividing barrier in the middel, then that makes the the offside lane of the anti-clockwise lane a radius 18 metres less than the nearside lane of the clockwise one.

As we know the circumference of the clockwise one, we can work out its average radius as follows:

c = 2x pi x radius, so 118 = 2 x 3.147 x r, therefore r = 118/(2x3.147) or 18.7 miles (29,997 meters).

So, using the radius of the nearest lane to the centre, the circumference is 2 x 3.147 x (29,997-18) or 117.93 miles.

So, the answer is the the inner most lane is 0.07 miles shorter than the outer most lane if the above assumpitions on lane width are correct, there are only 3 lanes on each side and excluding any points where the carriageways diverge (tunnels, QE2 bridge,etc).

Edited by youngsyr on Thursday 14th May 16:58

[rev-erend]

How do you sleep at night

Next question - World poverty .. off you go

Oh .. another .. The Female mind.. that might take longer

[mrmr96]

youngysr, you're nearly there but if you use more algebra you get a better answer (IMO).

r(a) = radius anti clockwise
r(c) = radius clockwise
c(a) = circumference anti clockwise
c(c) = circumference clockwise

c(a) = 2 * pi * r(a)
c(c) = 2 * pi * r(c)

A standard lane is 3.6m wide. So, assuming 3 lanes each way, plus 3.6m for the central reservation means there are 6 x 3.6m between the middle of lane one on each carriageway. Which is 21.6 meters.

So r(c)=r(a)+21.6
So:

c(c)-c(a)= (2 * pi * r(c)) - (2 * pi * r(a))
= 2 * pi * (r(c)-r(a))
= 2 * pi * (r(a)+21.6-r(a))
= 2 * pi * 21.6
= 135.7 meters
= 0.08 miles

(pi is approx 3.14159265 btw)

Edited by mrmr96 on Thursday 14th May 16:52

[youngsyr]

mrmr96 said:

youngysr, you're nearly there but if you use more algebra you get a better answer (IMO).

r(a) = radius anti clockwise
r(c) = radius clockwise
c(a) = circumference anti clockwise
c(c) = circumference clockwise

c(a) = 2 * pi * r(a)
c(c) = 2 * pi * r(c)

A standard lane is 3.6m wide. So, assuming 3 lanes each way, plus 3.6m for the central reservation means there are 6 x 3.6m between the middle of lane one on each carriageway. Which is 21.6 meters.

So r(c)=r(a)+21.6
So:

c(c)-c(a)= (2 * pi * r(c)) - (2 * pi * r(a))
= 2 * pi * (r(c)-r(a))
= 2 * pi * (r(a)+21.6-r(a))
= 2 * pi * 21.6
= 135.7 meters
= 0.08 miles

(pi is approx 3.14159265 btw)

Edited by mrmr96 on Thursday 14th May 16:52

You worked it out exactly the same way as me, mate just using a more accurate lane width (3.6m as opposed to 3m) and you got the correct number for pi, for some reason I thought it was 3.147!

The methodology is identical and equally open to inaccuracy in its assumptions, particularly the variation in lane width of between 2 and 8 lanes in places.

[pembo]

it's not a complete circle though, there are right and left turns in both directions so basing your calculations on it being a perfect circle would surely give a wrong answer

[mrmr96]

I see your edit now says 0.07 miles where previously you'd written about 0.4 hadn't you?