Pulling a truck (maths physics question)
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growingvegetables
Guru
- Location
- Leeds
... and he's forgotten summat else. If he gets it moving, he's got a 40 tonner on his tail ... with no brakes. Gotta keep going to the uphillYou've forgotten to release the trailer brake.
twentysix by twentyfive
Clinging on tightly
- Location
- Over the Hill
[QUOTE 4941929, member: 9609"]My question is really the maths and physics behind the problem[/QUOTE]
Without going into checking out all your arithmetic I don't see any glaring errors with the methodology. Where did the truck resistance number come from?
Without going into checking out all your arithmetic I don't see any glaring errors with the methodology. Where did the truck resistance number come from?
His calcs on power developed by a cyclist seem correct, as does the force needed to overcome tyre resistance. Wiki suggests figures of between 0.0045 and 0.008 for truck tyres, so 0.006 is in the ball park. However, is that for one tyre? Presumably we're talking about a lorry with more than one tyre. <lightbulb> but the normal force of the lorry is distributed through all the tyres, so it should be OK.
twentysix by twentyfive
Clinging on tightly
- Location
- Over the Hill
Of course the lorry needs that big engine because most of the time it's pushing a lot of wind. Then there are the hills........
[QUOTE 4941929, member: 9609"]I did mention in the OP to ignore the stiction (It would need a nudge to get it moving) and also the problems in getting traction, (may be a trike with a loaded rear axle)
But one thing is absolutely for certain you could pull one with a specially designed pedal powered machine if you got the gearing correct, you can pull one forward with a Sylvester and a length of scaf (I have done so with one loaded at 38t)
My question is really the maths and physics behind the problem - The figure I have come up for how much power I can deliver seems reasonable, but I'm thinking the 200w to move a 44 t lorry seems very very low. I have no intention of building such a macine and if I never seen another lorry I would be more than happy - it is no more than an interesting puzzle that popped into my head.[/QUOTE]
I think pulling a truck with a Sylvester (I'm guessing that's something like a Tirfor) will be happening at speeds well below 0.17mph (that's 0.08 m/s), so less power will be needed.
But one thing is absolutely for certain you could pull one with a specially designed pedal powered machine if you got the gearing correct, you can pull one forward with a Sylvester and a length of scaf (I have done so with one loaded at 38t)
My question is really the maths and physics behind the problem - The figure I have come up for how much power I can deliver seems reasonable, but I'm thinking the 200w to move a 44 t lorry seems very very low. I have no intention of building such a macine and if I never seen another lorry I would be more than happy - it is no more than an interesting puzzle that popped into my head.[/QUOTE]
I think pulling a truck with a Sylvester (I'm guessing that's something like a Tirfor) will be happening at speeds well below 0.17mph (that's 0.08 m/s), so less power will be needed.
twentysix by twentyfive
Clinging on tightly
- Location
- Over the Hill
This looks to be a struggle. He starts from speed = zero tho'
https://recordsetter.com/world-record/heaviest-vehicle-pulled-while-wearing-roller-skates/11797
https://recordsetter.com/world-record/heaviest-vehicle-pulled-while-wearing-roller-skates/11797
Wobblers
Euthermic
- Location
- Minkowski Space
[QUOTE 4941800, member: 9609"]I was trying to work out if it would be possible to pull a truck with a bike and what gearing would be needed. I have come up with the following but have zero confidence that I will have got my sums and theorys right
First of all lets ignore 'stiction' and also ignore the bike tyre and wheel being able to deliver the energy.
So here is the nonsense I have come up with.
my climbing limit at my favoured cadence is a 400' climb over 0.9 miles that I do at 5.5mph (39t driving a 32 rear)
me and bike 100kg
122m *x 9.81g x 100kg = 120,000 joules
= 203 watts
44 ton lorry tyre resistance 0.006
force need to overcome resistance = 2590 newtons
If I got it rolling at at 0.17mph the energy needed would be 206 watts which is close to my power output (it does seem a very low figure to move 44t so probably wrong 2000w may be more like it?)
for me to ride bike at my cadence and achieve 0.17mph
i would need 15t chainring driving a whopping 400t rear cog.
I doubt any of the above is correct but what would be the correct answer and where have I went wrong with the above scribblings ?[/QUOTE]
If we're going to look at this simplisitcally,
Energy = Force X Distance
In terms of power:
Power = Force X velocity
The force needed to overcome the rolling resistance of the truck tyres is (from your figures) 2590 N.
Velocity = 0.17 mph or 0.076 m/s
required power = 2590 X 0.076 = 196 W
Not very much, but not that surprising: they used to tow fully laden barges along canals with one person or one pony - and drag from the water is significant, even at fairly low speeds.
There's one small drawback. In order to generate the needed 2590 N force, the driving tyre of must be able to exert 2590 N against the ground. It has to be loaded with at least 264 kg in order to do so, otherwise it'll just skid. You cannot ignore the reaction forces acting on the tyre. So if you ensure that the rear wheel is weighed down at least 264 kg it would be possible to exert sufficient force as long as the gear ratio is large enough. Except... you can't ignore stiction, either. That increases the forces required several fold, at least.
First of all lets ignore 'stiction' and also ignore the bike tyre and wheel being able to deliver the energy.
So here is the nonsense I have come up with.
my climbing limit at my favoured cadence is a 400' climb over 0.9 miles that I do at 5.5mph (39t driving a 32 rear)
me and bike 100kg
122m *x 9.81g x 100kg = 120,000 joules
= 203 watts
44 ton lorry tyre resistance 0.006
force need to overcome resistance = 2590 newtons
If I got it rolling at at 0.17mph the energy needed would be 206 watts which is close to my power output (it does seem a very low figure to move 44t so probably wrong 2000w may be more like it?)
for me to ride bike at my cadence and achieve 0.17mph
i would need 15t chainring driving a whopping 400t rear cog.
I doubt any of the above is correct but what would be the correct answer and where have I went wrong with the above scribblings ?[/QUOTE]
If we're going to look at this simplisitcally,
Energy = Force X Distance
In terms of power:
Power = Force X velocity
The force needed to overcome the rolling resistance of the truck tyres is (from your figures) 2590 N.
Velocity = 0.17 mph or 0.076 m/s
required power = 2590 X 0.076 = 196 W
Not very much, but not that surprising: they used to tow fully laden barges along canals with one person or one pony - and drag from the water is significant, even at fairly low speeds.
There's one small drawback. In order to generate the needed 2590 N force, the driving tyre of must be able to exert 2590 N against the ground. It has to be loaded with at least 264 kg in order to do so, otherwise it'll just skid. You cannot ignore the reaction forces acting on the tyre. So if you ensure that the rear wheel is weighed down at least 264 kg it would be possible to exert sufficient force as long as the gear ratio is large enough. Except... you can't ignore stiction, either. That increases the forces required several fold, at least.
ColinJ
Puzzle game procrastinator!
- Location
- Todmorden - Yorks/Lancs border
classic33
Leg End Member
Uphill, on an "over-engineered bicycle".
KneesUp
Guru
Especially if going downhill.
classic33
Leg End Member
Getting out of the way, should he need to in a hurry, becomes a priority.
