The Motor Boat

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Aqueous Id said:
The boat speed is relative to both.

In this problem the boat speed is relative to the water and the water speed is relative to the bank. As long at the water is still, the boat speed relative to the water = the boat speed relative to the bank. But when the boat enters a current, that scenario changes. Now the speed relative to the water is still 8 km/hr but the boat speed relative to the bank is -3.27 km/hr ± 8 km/hr , depending on the direction of the boat.
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Not! You are trying to linearly transform the speed of the boat in still water to the speed of the boat in current. That's not how it works!
 
I guess Pete didn't think using flowing water in an example would be a problem.
One of the things about river flow is that it isn't constant across the width of a river, so you can reason that, in this example, the boat stays in the middle so the current is fairly constant and also assume the 5 km stretch the boat travels along is nice and straight.

Which is to say, when presented with a problem that looks like it has a linear solution, don't assume there are any nonlinear effects in play.
Or perhaps, to avoid any confusion, replace the river with something that is linear, say a 5km long treadmill big enough for a car, or something.
Or just place the river and treadmill in the same set of physical objects that represent surfaces on which things can travel, and leave it there.

Or not.

I mean, how much fun could there be in doing that?
 
arfa brane said:
Or perhaps, to avoid any confusion, replace the river with something that is linear, say a 5km long treadmill big enough for a car, or something.
Or just place the river and treadmill in the same set of physical objects that represent surfaces on which things can travel, and leave it there.

Or not.

I mean, how much fun could there be in doing that?
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I'm game! Sounds like a dyno to me!
 
arfa brane said:
I can't help but notice how some people just don't appreciate sarcasm . . .
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Did you ever think that one could think they are being cleverly sarcastic, but in reality nobody gets it? So if the "sarcasm" is not "gotten" then is it good sarcasm, or crap?
 
in my opinion motor daddy is correct in assuming the boat speed is referenced to the embankment.

he is wrong though in comparing a static treadmill (one that is human powered) to a dyno.

the correct analogy for the OP would be a powered treadmill and a battery powered toy car, scaling each appropriately.
you could however use a full scale model.
 
leopold said:
in my opinion motor daddy is correct in assuming the boat speed is referenced to the embankment.

he is wrong though in comparing a static treadmill (one that is human powered) to a dyno.

the correct analogy for the OP would be a powered treadmill and a battery powered toy car, scaling each appropriately.
you could however use a full scale model.
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The "correct" analogy would be to place an engine on a dyno and measure the torque@RPM so that you know the maximum load that can be placed on the crank at every RPM. Once the torque is known at every RPM then the Power is know by the equation HP=Torque*RPM/5252. 1 HP=550 ft-lb of WORK PER SECOND!
 
Motor Daddy said:
The "correct" analogy would be to place an engine on a dyno and measure the torque@RPM so that you know the maximum load that can be placed on the crank at every RPM. Once the torque is known at every RPM then the Power is know by the equation HP=Torque*RPM/5252. 1 HP=550 ft-lb of WORK PER SECOND!
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yes, this would give you the power output of the engine.
it will not tell you how much of that power is being used to propel the car, boat, plane, or brain fart.

we will need to make another assumption:
the power applied to the prop is such that the prop always turns at a certain RPM.

i think the treadmill/ toy car scenario is the best one to analyze the problem.
 
leopold said:
yes, this would give you the power output of the engine.
it will not tell you how much of that power is being used to propel the car, boat, plane, or brain fart.

we will need to make another assumption:
the power applied to the prop is such that the prop always turns at a certain RPM.

i think the treadmill/ toy car scenario is the best one to analyze the problem.
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But the prop DOESN'T always turn at a certain RPM upstream and downstream. If the prop turns at a different RPM and different load then what is the power, different, or the same??
 
Motor Daddy said:
Aqueous ID said:
Now the speed relative to the water is still 8 km/hr but the boat speed relative to the bank is -3.27 km/hr ± 8 km/hr , depending on the direction of the boat.
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Not! You are trying to linearly transform the speed of the boat in still water to the speed of the boat in current. That's not how it works!Not! You are trying to linearly transform the speed of the boat in still water to the speed of the boat in current. That's not how it works!
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That's exactly how it works.

Let's put the motor boat in a 50m swimming pool (it's a little electric RC boat).
You time it to take 22.5 seconds to go from one end to the other.

So, the boat is moving at 8 km/h in still water, right?


But, there's a catch - the pool is actually on a cruise ship, which is currently being tugged through the harbour at 3.27 km/h.

So, in the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
So, the little boat actually moves 70.4 metres if it's moving in the same direction as the ship (downstream), but only 4.6 metres if it's moving in the other direction (upstream).

So how fast is the little boat actually moving? 8 ± 3.27 km/hr
Does the little boat's motor RPM change depending on which way it goes? No, of course not.

Is a body of water carried in a swimming pool on a cruise ship equivalent to a body of water carried in a smooth current? Yes. The water in the middle of the pool doesn't 'know' whether it's in a pool or in a current - it's just carried along by the water around it in either case.
 
Pete said:
That's exactly how it works.

Let's put the motor boat in a 50m swimming pool (it's a little electric RC boat).
You time it to take 22.5 seconds to go from one end to the other.

So, the boat is moving at 8 km/h in still water, right?


But, there's a catch - the pool is actually on a cruise ship, which is currently being tugged through the harbour at 3.27 km/h.

So, in the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
So, the little boat actually moves 70.4 metres if it's moving in the same direction as the ship (downstream), but only 4.6 metres if it's moving in the other direction (upstream).

So how fast is the little boat actually moving? 8 ± 3.27 km/hr
Does the little boat's motor RPM change depending on which way it goes? No, of course not.
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:)

The pool is the embankment, right?
 
Motor Daddy said:
The pool is the embankment, right?
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Not really.
The bank of the river would be the same as a stationary frame of reference relative to the ship (and the pool on the ship), say, a wharf.
 
arfa brane said:
Not really.
The bank of the river would be the same as a stationary frame of reference relative to the ship (and the pool on the ship), say, a wharf.
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When I say the term "embankment" that is a term used to describe the Einstein embankment, which is clearly at a zero velocity in space, as measured by light.
 
Motor Daddy said:
The pool is the embankment, right?
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The embankment of the harbour is the embankment.

Motor Daddy said:
When I say the term "embankment" that is a term used to describe the Einstein embankment, which is clearly at a zero velocity in space, as measured by light.
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Well, the pool is being carried by the cruise ship at 3.27 km/hr. So no, it's not the embankment.
 
Motor Daddy said:
What does the velocity of the ship/pool have to do with how much time you measured the toy boat to travel from one side of the pool to the other?
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Nothing! It has no effect at all.
The boat still takes the same time to get from one end to the other, and the motor works just as hard, regardless of which way the water it's floating in is moving.
 
Pete said:
Nothing! It has no effect at all.
The boat still takes the same time to get from one end to the other, and the motor works just as hard, regardless of which way the water it's floating in is moving.
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You're missing the point of the current. The current is an opposing force to the boat's motion. The current slows the boat down when it's going upstream against the current. What current is opposing your toy boat's force in the pool?
 
Motor Daddy said:
You're missing the point of the current. The current is an opposing force to the boat's motion. The current slows the boat down when it's going upstream against the current. What current is opposing your toy boat's force in the pool?
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The water in the pool is moving at 3.27 km/h. Right?

In the 22.5 seconds it takes the boat to go the length of the pool, the whole pool moves 20.4 metres.
Right?

So in the 22.5 seconds it takes the boat to go the length of the pool, how far does it actually move, if it's moving in the same direction as the ship?
How far does it actually move, if it's moving in the opposite direction to the ship?
 
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