Speed (?)

[saywatt]

Assuming we have 2 identical cars running in a straight line (same direction): car A running at top speed (rev limit) and car B closely following car A at a lower speed, but accelerating. Is there any possibility for car B to overtake? I presume that it's not possible no matter how great its acceleration is because it would mean to exceed the top speed.

[swansont]

If they have the same max speed then no.

 

The wording of your set-up may impact the visualization of the problem: having car B "closely following" is difficult to reconcile with the fact that it is also traveling at a lower speed. If A is going faster, the distance between the cars will increase. Once after B reaches top speed, the distance between them will be constant.

[saywatt]

Thank you.

 

Yes, they have the same speed.

[J.C.MacSwell]

Assuming we have 2 identical cars running in a straight line (same direction): car A running at top speed (rev limit) and car B closely following car A at a lower speed, but accelerating. Is there any possibility for car B to overtake? I presume that it's not possible no matter how great its acceleration is because it would mean to exceed the top speed.

Any possibility? If B has same maximum then A must slow down for B to overtake A.

[gabrelov]

Assuming we have 2 identical cars running in a straight line (same direction): car A running at top speed (rev limit) and car B closely following car A at a lower speed, but accelerating. Is there any possibility for car B to overtake? I presume that it's not possible no matter how great its acceleration is because it would mean to exceed the top speed.

 

It said to identical cars so definitely their capabilities are the same therefore the distance between them not get lesser but much farther as car B accelerates until such point speed of both cars A and B are equal..

Edited August 12, 2013 by gabrelov

[Delbert]

Is there any possibility for car B to overtake?

Yes there is. I think you will find in racing circles it's called 'leapfrogging'.

 

It works because by slipstreaming vehicle A, vehicle B will gain speed. At the same time and because in physics nothing comes free, vehicle A will lose speed. Lose speed by the simple mechanism of the close proximity of vehicle B adversely upsetting the airflow around vehicle A. If that speed difference is sufficient for an overtake the vehicles will simply exchange places. The procedure will then repeat.

 

Needless to say such requires skill and precise timing by the drivers.

 

It will also require a long enough section of straight racetrack.

 

P.S. it's easier to achieve with two motorcycles.

[imatfaal]

Yes there is. I think you will find in racing circles it's called 'leapfrogging'.

 

It works because by slipstreaming vehicle A, vehicle B will gain speed. At the same time and because in physics nothing comes free, vehicle A will lose speed. Lose speed by the simple mechanism of the close proximity of vehicle B adversely upsetting the airflow around vehicle A. If that speed difference is sufficient for an overtake the vehicles will simply exchange places. The procedure will then repeat.

 

Needless to say such requires skill and precise timing by the drivers.

 

It will also require a long enough section of straight racetrack.

 

P.S. it's easier to achieve with two motorcycles.

 

The vehicle - especially if a cycle or motorbike actually gains speed if another slipstreams it. The back bike is not dragged along by the first - it merely takes advantage of a volume of air that is already been shifted from a steady state. The bike in front has its turbulence reduced because some of the air streams that would curl around him and cause drag are attached to the rider behind. At 40kph on a bike you can feel the saving in pedal power easily when you tuck in behind someone - and if you are really paying attention, and the follower is properly close you can persuade yourself you can feel a rider behind you joining in.

 

you might be able to find youtube of chris boardman (the olympic gold medallist and once (still?) the fastest man over an hour) and ned boulting (tv presenter) demonstrating this in a wind tunnel on the itv coverage of this years tour

[Delbert]

 

The back bike is not dragged along by the first - it merely takes advantage of a volume of air that is already been shifted from a steady state. The bike in front has its turbulence reduced because some of the air streams that would curl around him and cause drag are attached to the rider behind.

Think it's a matter of semantics what word is used.

 

And as I mentioned, the turbulence as you call it is also changed for the vehicle in front, thus increasing drag on vehicle A. Haven't you ever noticed when being tailgated down a motorway a slight drag effect?

[imatfaal]

Think it's a matter of semantics what word is used.

 

And as I mentioned, the turbulence as you call it is also changed for the vehicle in front, thus increasing drag on vehicle A. Haven't you ever noticed when being tailgated down a motorway a slight drag effect?

 

Not at all - we are saying the exact opposite. The lead bike GAINS from the following bikes slipstreaming - this is counterintuitive. It is to do with the fact that the follower is not being dragged but actually is moving in already disturbed air. The turbulence behind a singleton will slow it down - if that turbulence is reduced by having a close follower then the lead bike will suffer LESS drag than it would as a singleton

[Delbert]

I'm sorry, but I disagree with that.

[J.C.MacSwell]

Both can be correct. It depends on the quality of the airflow around the lead vehicle and how the presence of the following vehicle affects it.

 

For the average road vehicle a close following vehicle would usually decrease the drag of the lead vehicle. For a more aerodynamic vehicle with a well designed back end this may not be the case.

 

Often it will depend on the distance the 2 are apart.

[Delbert]

Sorry for my last abrupt reply as I was also dealing with three phone calls at the same time.

 

Anyway, aerodynamics is doubtless a complex issue if not mysterious, but all I know is that when I raced motorcycles for a while I couldn't achieve quite as high revs with someone close behind as I could otherwise.

 

And there's also what appears to me to be the physics of the situation; if the guy in front gains as well as the guy behind, who or what loses? There has to be loss somewhere as you can't get something for nothing. Or to put it another way, energy has to be obtained from somewhere if they both gain.

[imatfaal]

Sorry for my last abrupt reply as I was also dealing with three phone calls at the same time.

No worries - I write some of my best/worst posts when I am conference calling.

 

Anyway, aerodynamics is doubtless a complex issue if not mysterious, but all I know is that when I raced motorcycles for a while I couldn't achieve quite as high revs with someone close behind as I could otherwise.

I wonder, and the actual physics of this is a closed book to me, if the absolute speed makes a difference. If you go above 50 kph whilst slipstreaming on a pedal bike (which is the sort of bike I use) then it is pant-wettingly fast - whereas I am pretty certain you, on a motorbike, would be struggling to maintain interest at that speed; let alone at the more common high 30s low 40s kph

 

And there's also what appears to me to be the physics of the situation; if the guy in front gains as well as the guy behind, who or what loses? There has to be loss somewhere as you can't get something for nothing. Or to put it another way, energy has to be obtained from somewhere if they both gain.

In very simple terms; there is the mass effect of riding into a wall of air (fluids are accommodating - but only to an extent, try a belly flop) and in addition to that there is the fact that turbulent air streams behind you run quicker than undisturbed streams creating a tiny amount of lower pressure behind you (massive simplification). This is a retrograde force (and the actuality is much more complicated) but it means that the higly complicated air flow you have created around you will retard your motion to a small extent. However, if someone is following close behind the streams of air do not entirely detach from you and slow you down, what happens is that they are attached to the rider behind. The upshot is that the rider behind gets the massive benefit of riding in a "hole in the air" and picks up a minor discomfort of turbulent drag. The rider ahead gains nothing - but loses a negative, ie he loses the extra drag his turbulence is creating; losing a negative is positive and you go a little (and it really is a little) faster.

 

I think the reason you might not have noticed on motorbike racing is twofold. The massive speed might mean different stuff applies (are we talking 200kph?) and more importantly you are racing on a track. A track necessarily means serious bends (360+ worth in a few miles unless you are talking Isle of Man). A pedal bike race is completely different - I have ridden for an hour, in a team slipstreaming, for an hour without a single drop of pace; that's no corners, no brakes, full effort all the time. You could do that on a motorbike - but you would cover 200 miles! What I mean by the preceding is that (unless you are a complete bar-steward) you feel a responsibility and onus to be exact if you are in the front of a line; on a motorbike you have a few seconds to race and less time to react, on a pedal bike on a french avenue you have time to think and 5 minutes for your turn at the front.

[J.C.MacSwell]

 

And there's also what appears to me to be the physics of the situation; if the guy in front gains as well as the guy behind, who or what loses? There has to be loss somewhere as you can't get something for nothing. Or to put it another way, energy has to be obtained from somewhere if they both gain.

There is still a continuos energy requirement to maintain speed. It is just reduced. No laws of physics are broken.

[Delbert]

 

...there is the fact that turbulent air streams behind you run quicker than undisturbed streams creating a tiny amount of lower pressure behind you (massive simplification).

I'm not sure about that. For example, If I've a leak around the rear door of my estate car the air comes in with exhaust fumes. And by coming in would it not indicate a higher pressure and not lower as you say? Then there's this faster air stream at the rear you mention, since I'd have thought the fast air flow is the air going over the top centre of the vehicle - like the rounded top surface of an aircraft wing produces a lower pressure. In fact, I think if you go fast enough this lower pressure will lift you off the ground.

[MigL]

Sorry imatfaal, but as Dilbert said, turbulence over the top of a wing destroys lift, ie. the pressure increases and the wing stalls ( drops ). Same with the back of your vehicle or motorbike.

 

As for slipstreaming, if we assume that the only drag is caused by the air resistance ( disregard for the moment mechanical, rolling resistance etc. ), it takes a given amount of energy to do the work of moving the air out of the way. Unless you have completely laminar flow around rider A and rider B, there will always be some extra drag added by rider B to yhe lead rider A.. And since rider B will always see decreased drag ( some of the work has already been done by rider A ) then energy conservation dictates that drag for the lead rider A must increase.

[J.C.MacSwell]

energy conservation dictates that drag for the lead rider A must increase.

Sorry. But it does not. Vehicle B can both; benefit from the slipstream of A, and decrease the drag of A, in the right circumstance, by getting close enough to reduce the vacuum on the back of A

[MigL]

So if a jet airliner becomes uneconomical, don't re-engine it or switch to a larger one , just add another one in front of it and you'll reduce drag, increase speed and/or increase economy.

 

An airplane which has a max speed will be able to go faster or farther if fallowed by another plane.

 

As a matter of fact, the race to go supersonic in the late 40s/early 50s could have been avoided by flying a long string of piston engine airplanes instead of going to jets ,4% chord thickness airfoils, higher finesse ratios ,Whitcombe area ruling and variable shock inlets.

 

In other words, I don't believe you.

[J.C.MacSwell]

So if a jet airliner becomes uneconomical, don't re-engine it or switch to a larger one , just add another one in front of it and you'll reduce drag, increase speed and/or increase economy.

 

An airplane which has a max speed will be able to go faster or farther if fallowed by another plane.

 

As a matter of fact, the race to go supersonic in the late 40s/early 50s could have been avoided by flying a long string of piston engine airplanes instead of going to jets ,4% chord thickness airfoils, higher finesse ratios ,Whitcombe area ruling and variable shock inlets.

 

In other words, I don't believe you.

If you assume because it won't work for aerodynamic shapes, then it won't work for bluff bodies, it might be difficult to convince you.

[J.C.MacSwell]

If you assume because it won't work for aerodynamic shapes, then it won't work for bluff bodies, it might be difficult to convince you.

From http://en.wikipedia.org/wiki/Drafting_(aerodynamics)

 

 

Drafting or slipstreaming is a technique where two vehicles or other moving objects are caused to align in a close group reducing the overall effect of drag due to exploiting the lead object's slipstream. Especially when high speeds are involved, as in motor racing and cycling, drafting can significantly reduce the paceline's average energy expenditure required to maintain a certain speed and can also slightly reduce the energy expenditure of the lead vehicle or object.

Edited August 25, 2013 by J.C.MacSwell

[MigL]

I do agree with the first part of the wiki definition that the 'average energy expenditure of the paceline is reduced' JC. however I have trouble with the second part that 'can also slightly reduce energy expenditure of the lead vehicle. This would only be possible with laminar flow over the paceline, once turbulence is introduced between vehicles, I do not see how it is possible.

 

Ever see migrating geese JC ? They use a modified slipstream effect ( v formation ) to make the journey easier for the following geese. The lead goose is rotated out every so often because his workload is increased. If it was reduced compared to individual flight there would be no reason for this.

 

I'm open to a convincing argument with examples,JC, but don't expect me to agree with you because 'wiki says so'.

[J.C.MacSwell]

I do agree with the first part of the wiki definition that the 'average energy expenditure of the paceline is reduced' JC. however I have trouble with the second part that 'can also slightly reduce energy expenditure of the lead vehicle. This would only be possible with laminar flow over the paceline, once turbulence is introduced between vehicles, I do not see how it is possible.

 

Ever see migrating geese JC ? They use a modified slipstream effect ( v formation ) to make the journey easier for the following geese. The lead goose is rotated out every so often because his workload is increased. If it was reduced compared to individual flight there would be no reason for this.

 

I'm open to a convincing argument with examples,JC, but don't expect me to agree with you because 'wiki says so'.

At some point outside the turbulence the flow essentially remains laminar. Reducing the turbulent regime even slightly will generally reduce the drag. It is not all or none.

 

http://papers.sae.org/2004-01-1145/

 

From the abstract (which is free) bolded by me:

 

"We demonstrate the interaction of two truck shapes in tandem. Both trucks experience a decreased drag coefficient from the interaction. The degree of drag saving depends strongly upon the drag coefficients of the model trucks in isolation, and upon how the two trucks are arranged. For the two simplest shapes-parallelepipeds with or without partial leading-edge rounding-the total drag saving can range from 10 percent to 40% at a spacing of 2√A (approximately 18 feet at full scale) depending upon whether the lead or the trail parallelepiped has rounding. These two shapes-blunt and rounded-have drag coefficients in isolation of 0.94 and 0.51 respectively, and probably bracket the savings to be obtained for all real truck geometries."

 

Would you really remain the lead goose knowing your buddies are benefiting much more than you are?

[imatfaal]

I do agree with the first part of the wiki definition that the 'average energy expenditure of the paceline is reduced' JC. however I have trouble with the second part that 'can also slightly reduce energy expenditure of the lead vehicle. This would only be possible with laminar flow over the paceline, once turbulence is introduced between vehicles, I do not see how it is possible.

 

Ever see migrating geese JC ? They use a modified slipstream effect ( v formation ) to make the journey easier for the following geese. The lead goose is rotated out every so often because his workload is increased. If it was reduced compared to individual flight there would be no reason for this.

 

I'm open to a convincing argument with examples,JC, but don't expect me to agree with you because 'wiki says so'.

 

You are not willing to accept wiki - fine - but you don't get to make assertions about the motivations of geese. I can tell you that with cyclists (who you can quiz about motivation) the reason that you rotate down a pace line is so that you get a higher average speed. If you do not rotate you get to your destination 50km away at the average speed of a lone cyclist (plus or minus a bit + JCMac/my position or - yours/Delberts) doing 50km. If you rotate you get there at the speed of the leader cyclists putting in 500-1000m dashes (then he/she rests in the line) which can be considerably higher. 8/9 riders can probably average 5% higher speed over a 50km course. You put in spells at the front in turn not so much because the man at the front is tired - but because the riders behind are rested (I realise it seems like the same thing - but it isnt.)

[MigL]

You're right Imatfaal, I'm not a goose.

And you and JC are most likely right ( I have to concede ).

But it was an interesting ( and pleasant ) discussion.

[imatfaal]

most agreeable - and talking of slipstreaming and such like - did any one see the Ulster Grand Prix? The benefits to the follower (regardless of the leader) couldn't be more clear than in long open road-race circuits and high powered bikes. Back and forth two or three riders over-taking and re-taking position - all down to getting the slipstream right and sling-shotting them past the leader (and being as brave as possible and highly skilled. At least two races I watched finished with less than a tenth between podium positions - and it came down to lines in tight corners and ability to slip-stream. Totally OT why do we bother with car racing when bike racing is so much more fun.