BX Power to Weight Ratios

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Des Smith
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Post by Des Smith » Sat Feb 25, 2012 12:18 pm

Defender110 wrote: Indeed they did with a VV Beatle being dropped from one mile high and pip squeak trying to beat it to its landing point from one mile away in a Porche 911.
Yup, but that is not the same as seeing which of two or more cars reach the ground first. Let's not upset anyone by suggesting this hypothesis be tested with virtual BXs, but we could use the TG premise of a 911 v Beetle.

I guess the calculation would be acceleration due to gravity (9.81185m/s/s as I recall) less resistance due to air and aerodynamic efficiency plus some accounting of the attitude of the car as it is now moving in three dimensions. There's also the launch speed to factor in as well. That is a sum well beyond my competency (Physics O Level Grade B), but if anyone fancies booting that one around, I'd be curious to see the hypothetical answer.

This line of thinking has lurked at the back of my mind ever since the Lambretta flew of Beachy Head in 'Quadrophenia'. I always felt a decent bike would have reached the sea while the scooter was a predictable underachiever. :lol: :lol: :lol:
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Post by BX Meteor » Sun Feb 26, 2012 3:55 am

/\ we need to know
(a) the terminal velocity for a BX
(b) the time it takes to reach that terminal velocity
(c) the distance travelled to reach that terminal velocty
(d) then we can work out the remaining distance to travel at that terminal velocity, and hence the time over that remaining distance
(e) the total time taken will be time from (b) plus time from (d)

For this, we need to use

Newton's 3 equations of motion
1a) v= u + at
1b) s = ut + ½at²
1c) v² = u² + 2as

Newton's 2nd law of motion
2) F=ma

and the force acting on a body due to aerodynamic drag
3) F = ½ ρ C A v²

[ .... in the above equations
ρ is the air density (1.293 at STP)
C is the drag co-efficient of the body (say 0.34 for a BX falling nose first)
A is the cross-sectional area of the body (say 2.4 m² for a BX falling nose first)
m is the mass of the body (say 1000 kg for a BX)
v is the terminal velocity of the body in m/s
u is the initial velocity of the body in m/s (say 0)
t is time over the interval in question in secs
s is the distance over the interval in question in metres
a is acceleration due to gravity (9.811 m/s²) ..... ]


At terminal velocity, equations (2) and (3) are balanced

so ma = ½ ρ C A v²
i.e. v² = ma ÷ (½ ρ C A) = 1000 x 9.81 ÷ (½ 1.293 x 0.34 x 2.4) = 9811 ÷ (0.527544) = 18597.5
answer (a) v = 136 m/s (306 mph)

although the acceleration due to gravity will reduce as the drag builds up, to keep is simple we can use equations 1a and 1c to calculate the time and distance to reach the terminal velocity
answer (b) t = (v-u) ÷ a = 136 ÷ 9.811 = 13.86 secs
answer (c) s = v² ÷ 2a = 18597.5 ÷ (2 x 9.811) = 948 metres

To get the remaining distance, 1 mile = 1609 metres, it has fallen 948 metres, so there are 661 metres to fall at 136 m/s

answer (d) remaining time = 661 ÷ 136 = 4.86 secs

answer (e) the total time for a BX to fall nose first from 1 mile up = 13.86 + 4.86 = 18.72 seconds ...... and it hits the ground at 306 mph ... these answers assume we fit streamers from the rear wing to stop it tumbling




In top gear they estimated that the Beetle would take between 36 to 40 secs to fall 1 mile

Image

The reason it takes 36 to 40 secs is that they dropped it with wheels facing downwards

Image

and Richard Hammond says that it reaches a terminal velocity of 125 mph (but it tumbles as it drops)

Image



The easiest way to estimate a car dropping in that way, is to take A as the cross-sectional area of the underside, and use a vale for C of about 2.1 (a square box)

I'll let someone else do that, just repeat what I did, but use the new values (I now wish I'd done it in a spreadsheet rather than on the back of an envelope, and I can't be arsed to copy my typing with new numbers).




For a scooter going off Beachy head (160 metres high)
.... we only require equations 1b and 1a because I doubt if it reaches terminal velocity (assuming again a constant acceleration, to keep it simple)
[ also, it's difficult to work out whether ithe scooter would reach terminal velocity, because the co-efficient of drag for a tumbling scooter could continually vary between 0.6 (nose down) and 1.4 (similar to horizontal skydiver), with varying cross-section. Maybe try it wheels down with C of 1.4 and measure the underside of a scooter for cross-section, then do (a), (b), (c) to see if it reaches terminal veocity in less than 160 metres. But I reckon it hits the ground before reaching terminal velocity ]

Using equation 1b
s = ut + ½at²
u is the initial vertical velocity, which is zero. s is the height, which is 160.

so 160 = 0 + ½ 9.811 x t²
i.e. t² = 32.616, so t = 5.711 secs

using equation 1a
v = u + at = 0 + 9.811 x 5.711 = 56 m/s = 126 mph

The horizontal distance depends on the horizontal speed just before it leaves the top. Say 60mph i.e. 100 kph i.e. 27 m/s.

It falls for 5.711 secs, and to keep it simple assume the drag doesn't reduce its horizontal speed in that time.

So horizontal distance travelled = 27 x 5.711 = 154 metres

i.e. it keeps travelling horzontally at 60 mph, while it accelerates vertically from 0 to 126 mph, hitting the ground 5.711 seconds later, having fallen 160 metres and travelled 154 metres from the cliff bottom (assuming a vertical cliff).

In 'Quadrophenia', it looked to me as if they secured the handlebar stem to limit the steering, set the throttle at say half way, then someone stood at the side and pulled the clutch lever, moved it to say 1st gear then let the clutch out as they ran alongside and then left it to go over the cliff. They would have decided where they wanted it to hit the ground so the cameraman would be in the right place, then knowing the horizontal distance from cliff bottom and the time it takes to fall, you work out the horizontal speed you want it to leave the top of the cliff (10 mph would be ~25 metres)

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Post by mds141 » Mon Feb 27, 2012 10:38 pm

..that_
Mark Smith

Is it just me or is everything shit?

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Post by BX Meteor » Wed Feb 29, 2012 1:38 am

Link to a spreadsheet can be found here

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Post by Kitch » Thu Mar 01, 2012 7:40 pm

BX 14 = eager and willing but ultimately slow.
BX 16 = slightly less eager but slightly faster.
BX 17D = very slow but steady
BX 17TD = in gear, once the turbo's spooled up it's fine. Any other time it's flat.
BX 19 = torquey enough to keep up with modern traffic without needing special effort. Nice and flexible, plus refined.
BX 19D = willing at all times, but will still likely hold up vans on the motorway.
BX 19i = fairly flexible, pretty grunty, bit breathless and harsh at the top end
BX 16v = as willing as 19i 8v at low revs but only betters it if you cain the arse off it.

There ya go. Simple.

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Post by Mothman » Thu Mar 01, 2012 8:15 pm

BX 19D = willing at all times, but will still likely hold up vans on the motorway.

Only going uphill, will happily cruise at 80 all day, same as the TD.Oh, and the 1.6 petrol, well, faster than both.

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Post by Kitch » Thu Mar 01, 2012 8:34 pm

Grenman wrote:BX 19D = willing at all times, but will still likely hold up vans on the motorway.

Only going uphill, will happily cruise at 80 all day, same as the TD.Oh, and the 1.6 petrol, well, faster than both.

Andy
Being able to cruise at 80mph isn't exactly a milestone in performance! And besides, I'd argue they can cruise at 80.....they'll sit at 80 but they're too vocal at that speed. Much happier at 70mph. TD is slightly longer legged, so yeah I'd say that'll cruise at 80mph all day long.
1.6 petrol faster than both? I wouldn't say so. N/A diesel yes, but it's about even with a TD overall. TD is quicker in a single gear, 1.6 is quicker when you're hammering the arse off it.

The only BX I haven't driven on that list is the 17D.

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Post by saintjamesy89 » Thu Mar 01, 2012 8:37 pm

Am I right in saying that a 16 Meteor is slightly more powerful than other 16's? Due to a difference in carbs or something?

Also how does the auto transmission effect these attributes?
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Post by Kitch » Thu Mar 01, 2012 8:44 pm

saintjamesy89 wrote:Am I right in saying that a 16 Meteor is slightly more powerful than other 16's? Due to a difference in carbs or something?

Also how does the auto transmission effect these attributes?
Not really, all 16's are there or there abouts the same. The 15 was a detuned 1600, and that's obviously slower. You might get one car drive nicer because the carb is in better nick, but nothing of note.

Auto tranmissions rape the 16 engine in my experience. I've had manuals and autos, and the manual although no speed record setter moved along with modern traffic without fuss and pulled 42mpg on a run. The auto was slower than a 1.9D estate (honestly) and struggled to better 20mpg. This was mainly because you were having to apply so much gas to get a response. The gearbox was just too tall for it. Better suited to the 19, which feels like it has a good deal more grunt under the bonnet. Still not a fast car, but a capable one with an auto box.

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Post by Dollywobbler » Thu Mar 01, 2012 9:26 pm

I used to sit at an indicated 80mph all the time in my BX 19TGD. It didn't sound strained at all. It did at 90mph, at which point I told my BXagon co-driver to ease up a bit! (I have clocked 100mph in one once, but it didn't seem to enjoy it).

To be honest, 80mph in my valver was more painful than the 1.9 diesel (4000rpm, sports exhaust, panel air filter. Not peaceful!).

Where the diesel really struggles is somewhere like Shrewsbury, where you've got dual carriageway with lots of roundabouts. The NA diesel just doesn't have the power to quickly get up to speed. Oh, and steep hills!

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Post by BX Meteor » Thu Mar 01, 2012 10:38 pm

And don't forget that the speedometers in these cars read about 10% high (check it against satnav or road angel etc)

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Post by Des Smith » Thu Mar 01, 2012 11:25 pm

saintjamesy89 wrote:Also how does the auto transmission effect these attributes?
Makes it dog slow. You can boil a kettle in the time it takes to get to 30! You're better off with a bicycle...

There you go, I've had a long shitty day and now I've pissed off half the forum!
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Post by Kitch » Fri Mar 02, 2012 10:24 am

Dollywobbler wrote:I used to sit at an indicated 80mph all the time in my BX 19TGD. It didn't sound strained at all. It did at 90mph, at which point I told my BXagon co-driver to ease up a bit! (I have clocked 100mph in one once, but it didn't seem to enjoy it).

To be honest, 80mph in my valver was more painful than the 1.9 diesel (4000rpm, sports exhaust, panel air filter. Not peaceful!).

Where the diesel really struggles is somewhere like Shrewsbury, where you've got dual carriageway with lots of roundabouts. The NA diesel just doesn't have the power to quickly get up to speed. Oh, and steep hills!
Oh yeah, the valver doesn't do cruising at anything more than 65mph! :lol: It does speeding very well, but not cruising.