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Sadurian Mike
641908.  Mon Nov 30, 2009 7:07 am Reply with quote

Hang on, are you saying that if I let go of a helium-filled balloon and an air-filled one at the same time, the helium-filled balloon will fall at the same rate as one filled with air? No floating or bobbing about?

If that is the case then a whole party-balloon industry is going to be very upset.

 
gruff5
641913.  Mon Nov 30, 2009 7:28 am Reply with quote

Think you out-klaxoned PDR there, Mike.

Your explanation of the ball flight makes sense to me and seems the obvious one.

 
PDR
641925.  Mon Nov 30, 2009 8:25 am Reply with quote

As ever, the fallen angel is in the detail (which is why I mentioned mas/drag ratio later in the post), although I seem to have been optimistic in leaving the matter as an exercise for the reader.

Two objects which actually have weight will fall at the same speed, until they approach their terminal velocity. An airfilled ballon has an extremely low terminal velocity, so it appears to fall more slowly than (say) a christmas pudding, but its initial acceleration will be exactly the same (with or without brandy flambe). A helium-filled balloon which has positive bouyancy (or negative weight) will still have a terminal velocity, but it may not be obvious as it will accelerate upwards rather than downwards. It is also not "falling" in the same sense.

The terminal velocity is a function of the mass/drag ratio. For a sphere the terminal velocity is given by:

v(terminal) = (2.m.g/C.rho.A)^0.5

(mass, acceleration due to gravity, drag coefficent of a sphere[0.5], air density, cross sectional area)

The mass/drag ratios of the air and helium-fulled footballs are both rather high and also very similar, because the weight differences between the balls would be less than 20grammes (you can check this for yourself by looking up the relative densities of air and helium at 2bar absolute pressure), whilst footballs weigh around 450grammes - so we're looking at a difference of around 5% at most. The actual terminal velocity of a football (22cm diameter, 430-450g mass) works out to over 600mph (assuming sea level air pressure and a perfect sphere). No kicker ever measured has achieved even a substantial fraction of this, so the effect of the terminal velocity issues on the velocity profile of the kicked ball will be negligible.

QED

KLAXON RESTORED

PDR

 
Sadurian Mike
641927.  Mon Nov 30, 2009 8:30 am Reply with quote

Sorry, you lost me in there.

Are you saying that a football filled with a gas that lifts it will fall at the same speed as a football filled with air that doesn't?

 
gruff5
641933.  Mon Nov 30, 2009 8:48 am Reply with quote

What's with all this deafening KLAXON-sounding ?

PDR wrote:
Objects will fall at the same rate regardless of their weight - a chap called Galileo demonstrated this by dropping things from a pizza hut.

Not quite. You don't need any maths or formulae to realise this isn't true. Galileo was disregarding air resistance, which is a legitimate thing to do when comparing iron cannonballs. But I think you can see it's not true for a falling feather vs. a falling lead weight?

PDR wrote:
Two objects which actually have weight will fall at the same speed, until they approach their terminal velocity.

No. Refer to my previous mention of feather and lead weight.

PDR wrote:
The actual terminal velocity of a football (22cm diameter, 430-450g mass) works out to over 600mph (assuming sea level air pressure and a perfect sphere).

I think there must be something up with your maths, PDR? The terminal velocity of a human body is about 160-180mph (I know, having freefallen from 12,000 feet!). I can't imagine a football tossed out of the aircraft at the same time would have overtaken me that easily, can you?!

 
PDR
641936.  Mon Nov 30, 2009 9:10 am Reply with quote

A standard football filled with air weighs 450g. Replacing the air with helium will reduce its weight by about 20g, so it now weighs 430g. You cannot make a football lighter than air by filling it with helium.

A 430g football will fall at the same speed as a 450g football until the airspeed gets to a sizable fraction of its terminal velocity - call it half. The terminal velocity of a football is something over 600mph, so unless they exceed 300mph there will be no significant difference in their velocity profile.

No human kicker will achieve a kick of 300mph in a horizontal direction, and to reach 300mph vertically the ball must fall through at least 900m (s=v^2/2a), which isn't going to happen either.

Therefore the falling characteristics will be much the same within the regions relating to the original premise (a kicked football).

PDR

 
Davini994
641943.  Mon Nov 30, 2009 9:30 am Reply with quote

I would guess that it's to do with coefficient of restitution rather than buoyancy. It does look like it might 'hang' a bit, but it's difficult to tell with any sort of certainty at all.

PDR wrote:
Two objects which actually have weight will fall at the same speed, until they approach their terminal velocity.

Are you sure? A quick sub into N2 solving for acceleration give different results with constant buoyancy force from constant volume.

Would a rugby ball pressure not be about 80psi?

 
PDR
641949.  Mon Nov 30, 2009 9:41 am Reply with quote

Davini994 wrote:
PDR wrote:
Two objects which actually have weight will fall at the same speed, until they approach their terminal velocity.

Are you sure? A quick sub into N2 solving for acceleration give different results with constant buoyancy force from constant volume.


Take two empty coke bottles. Put a 20g lead weight inside one of them and drop them - would the initial accelerations be the same? The terminal velocities would be different (marginally) because one has a different density, but the initial accelerations would be the same.

The feather example is a good one - in an earth-type atmosphere the feather has an extremely low terminal velocity (typically about 0.25m/sec) so it achieves this almost instantaneously. But in the much thinner atmosphere on the moon it has a terminal velocity of about 14,000mph, so a rock and a feather will fall at the same rate (demonstrated on the apollo XIV mission IIRC). A ball full of helium simply has a lower density - its acceleration due to gravity is unaffected.

Quote:

Would a rugby ball pressure not be about 80psi?


Possibly, but I took the standard figures for a football from the FISA website as a reference. It doesn't make a lot of difference.

PDR

 
PDR
641957.  Mon Nov 30, 2009 9:51 am Reply with quote

gruff5 wrote:
Not quite. You don't need any maths or formulae to realise this isn't true. Galileo was disregarding air resistance, which is a legitimate thing to do when comparing iron cannonballs. But I think you can see it's not true for a falling feather vs. a falling lead weight?


Why have you ignored the voluminous data on CALCULATING "air resistance" and then said I've missed that bit??

Quote:

PDR wrote:
Two objects which actually have weight will fall at the same speed, until they approach their terminal velocity.

No. Refer to my previous mention of feather and lead weight.


Yes. Refer to my posts on the subject of terminal velocity. The feather is a complete red herring in any event because air and helium-filled balls will have identical drag coefficients, and the drags will only differ slightly due to the (miniscule) difference in densities.

Quote:

PDR wrote:
The actual terminal velocity of a football (22cm diameter, 430-450g mass) works out to over 600mph (assuming sea level air pressure and a perfect sphere).

I think there must be something up with your maths, PDR? The terminal velocity of a human body is about 160-180mph (I know, having freefallen from 12,000 feet!). I can't imagine a football tossed out of the aircraft at the same time would have overtaken me that easily, can you?!


Of course it would. The 160mph terminal velocity of a human is when in the spread-eagled free-fall posture - if you pull in your limbs and re-orient into a vertical dive attitude your terminal velocity goes up to around 250mph (due to reduced drag coefficient). It's quite common for air-deployment teams to throw footballs, milk bottles and numerous other objects out of the back of herc when doing drop-exercises - milk bottles go supersonic on the way down (making an awesome noise, which why they do it) and footballs get close to supersonic, often showing scorch marks from the shock-heating.

This is all very basic physics - I'm surprised peiople have trouble with it.

PDR

 
gruff5
641960.  Mon Nov 30, 2009 10:06 am Reply with quote

PDR wrote:
.... footballs get close to supersonic, often showing scorch marks from the shock-heating.

Well, knock me down with a feather, I never knew this! I'm surprised that this is so, even taking into account the low drag of its spherical shape, since an inflated football is far less dense than a human body.

 
Davini994
641964.  Mon Nov 30, 2009 10:20 am Reply with quote

PDF wrote:
Take two empty coke bottles. Put a 20g lead weight inside one of them and drop them - would the initial accelerations be the same? The terminal velocities would be different (marginally) because one has a different density, but the initial accelerations would be the same.


Near enough true, because it has minimal volume so buoyancy is not a factor. For the football it's different.

Taking jolly simple numbers to demonstrate:

football filled with air: 5kg
football filled with helium 4kg

Buoyancy: same for both: 10N

gravitational force on air filled: 50N
gravitational force on helium filled: 40N

F =ma => a = F/m

(Overall force of course)

a air = 40N / 5kg =8 m/s
a helium = 30N/4kg = 7.5 m/s

While the variations will be bigger than reality, I think it demostrates the principle that buoyancy in principle a factor as well as drag. A small difference in the acceleration will give a proportionally larger difference in distance.

To repeat, this is the bit where I disagree with you:

Quote:
A ball full of helium simply has a lower density - its acceleration due to gravity is unaffected.

Because the acceleration is due to gravity less the buoyancy.

Objects tend to their terminal velocity to, they don't accelerate at a constant rate to get to it then stop accelerating.

PDF wrote:
This is all very basic physics - I'm surprised people have trouble with it.

Quite!

 
PDR
641969.  Mon Nov 30, 2009 10:36 am Reply with quote

gruff5 wrote:
PDR wrote:
.... footballs get close to supersonic, often showing scorch marks from the shock-heating.

Well, knock me down with a feather, I never knew this! I'm surprised that this is so, even taking into account the low drag of its spherical shape, since an inflated football is far less dense than a human body.


Density is one factor, but drag co-efficient is another. A rough sphere has a Cd of around 0.5 (the number I used), and a smooth sphere could be as low as 0.1 - the football will be somewhere between these two. The Cd of a skydiver in the spread-eagle position is usually around 1.3, with around 0.7 - 0.8 being experienced in the vertical dive position.

PDR

 
gruff5
642024.  Mon Nov 30, 2009 12:49 pm Reply with quote

PDR wrote:
Density is one factor, but drag co-efficient is another. A rough sphere has a Cd of around 0.5 (the number I used), and a smooth sphere could be as low as 0.1 - the football will be somewhere between these two. The Cd of a skydiver in the spread-eagle position is usually around 1.3, with around 0.7 - 0.8 being experienced in the vertical dive position.

Just got back from the gym and there was soccer happening on the TV screens that I couldn't help watching, being that the screens are right in front of the treadmill. Well, on the occasional, high-looping kicks across-field, it was plain to see that the ball was falling earthwards from the loop summit at nothing like the acceleration/velocity that you would expect for a human body. The maths involved in weighing up the balance of density vs. drag is not needed to debate what's in front of your nose.

Think if the soccer game was played not in a stadium, but in an open sports field. A modest breeze blows across from the side and the football is blown off course. Would this happen to a falling human body? Of course not. It would take winds approaching hurricane-force to send a human body appreciably away from falling straight down.

Do you have a reference for the 600mph (never mind scorched!!) falling footballs, PDR?

 
Davini994
642057.  Mon Nov 30, 2009 2:30 pm Reply with quote

A falling football isn't anywhere near terminal velocity though, as PDR has said it would need to fall through 900m or so to be near. They must fall at about the same, give or take a few percent.

I certainly wouldn't want to head the thing on a cold and wet day if it was doing 600mph...

 
Posital
642073.  Mon Nov 30, 2009 3:18 pm Reply with quote

Efros wrote:
Posital wrote:
If the gas content on a tyre can reduce fuel consumption, then perhaps this is possible somehow.
Reduction in tyre pressure produces increased contact of the tyre with the road, so more friction so less miles per gallon
Yes - quite.

There was recently a thing about filling tyres with noble gasses or some such.

 

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