Efficient acceleration

[hobz]

I have come across the statement that it is more efficient to accelerate a mass at the beginning of a total movement, than later on.

 

So having a mass at rest and wanting to accelerate it up to 10 m/s over 10 s, it should be more efficient to accelerate the mass to 10 m/s earlier on.

 

Why is this?

[traveler]

I have come across the statement that it is more efficient to accelerate a mass at the beginning of a total movement, than later on.

 

So having a mass at rest and wanting to accelerate it up to 10 m/s over 10 s, it should be more efficient to accelerate the mass to 10 m/s earlier on.

 

Why is this?

 

 

Force is created by the relativity of two object's motion.

 

It takes more power to create the same force at a higher speed.

 

It's the same thing with rotational velocity.

 

HP=torque*RPM/5252

 

20 lb-ft*20 RPM/5252=.076 HP

20 lb-ft*40 RPM/5252=.152 HP

 

Can you see the relationship between velocity and force?

[DrP]

Force is created by the relativity of two object's motion.

 

It takes more power to create the same force at a higher speed.

 

 

Presumably because of the v sqared in the equation for kinetic energy??

[CaptainPanic]

Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating:

 

[math]E = 0.5 * m * v^2[/math]

 

Where efficiency comes into play is indeed in things like torque and an engine's RPMs.

 

p.s. I must object to the use of nice rules of thumb like traveler has posted, because they are using silly units. Please use SI units whenever possible, it will avoid mistakes.

[traveler]

Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating:

 

[math]E = 0.5 * m * v^2[/math]

 

Where efficiency comes into play is indeed in things like torque and an engine's RPMs.

 

p.s. I must object to the use of nice rules of thumb like traveler has posted, because they are using silly units. Please use SI units whenever possible, it will avoid mistakes.

 

Silly units?

 

Really?

 

Who invented the unit of measure of power known as HP?

 

Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating:

 

[math]E = 0.5 * m * v^2[/math]

 

Where efficiency comes into play is indeed in things like torque and an engine's RPMs.

 

p.s. I must object to the use of nice rules of thumb like traveler has posted, because they are using silly units. Please use SI units whenever possible, it will avoid mistakes.

 

No "s" in the acronym RPM, it stands for Revolutions Per Minute. Adding an s means Revolutions per minutes.

 

Your above statement is completely wrong. Two exactly the same objects being accelerated at different acceleration rates to the same final velocity will take a different amount of time to get to that velocity. The object that increases velocity at the greatest rate has the most POWER.

Edited September 11, 2008 by traveler
multiple post merged

[Klaynos]

We're a science forum, it is accepted that in science SI units are used. But for the most part as long as we're clear about what units we're using we can all manage to understand each other.

 

Now, on topic...

 

The energy will indeed be the same as stated previously, and I suspect what is going on here is the device providing the energy is non-linear, so it'll be more efficient at some areas compared to others... I suspect a mechanical engineer would be alot better at going into the intricies of this, but I know that different motors as an example have significant efficiency differences.

 

Energy is the same as:

 

[math]E=\frac 1 2 mv^2[/math]

 

The power will be different as power is energy/unit time.

[CaptainPanic]

The reason I called the units silly is that I would need a few minutes perhaps to work out what the units are of the constant with the value 5252 in the formula:

 

HP=torque*RPM/5252

 

Especially if you would not have given the examples later, I would have been clueless which units to use for the torque. If I would have used the standard SI units (N m), I would not get the right answer.

 

The units of the constant will be lb*ft*RPM/HP... which is a bit of a mess to be honest.

 

the main problem shows up with converting the Torque. In SI, the units are (N m), which is (kg*m/s2) * m. The Imperial version is in lb*ft... which would convert to kg*m. Somewhere the gravitational constant (m/s2) has gone missing. It could also be lbf*ft (poundforce*feet)... but I haven't been able to doublecheck that (because I cannot be bothered, silly units).

 

In addition:

 

There have been a number of different "pounds" in the past, but the common definition I guess is 1 lb = 0.45359237kg.

You should note that there exists also a pound-force, which is 0.45359237 kg × 9.80665 m/s²

Then 1 ft = 0.30480 m.

Then we have the horsepowers according to wikipedia:

1 HP =745.6999 W

 

There are some more variations though:

Mechanical horsepower = 745.6999 W

Metric horsepower = 735.49875 W (exactly)

Electrical horsepower = 746 W

Boiler horsepower = 9809.5 W

 

So, let's just use the 1st one: 1 HP = 745.6999 W

 

Using the torque in lb*ft (and not lbf*ft).

Then we can derive that 5252 lb*ft*RPM/HP = 5252 * 0.45359237 * 0.30480 * (1/60) / 745.6999 = 0.0162 s2/m.

 

but I might be wrong, as I said before... the torque is just puzzling me.

 

If the torque is in pound-force:

5252 lb*ft*RPM/HP = 5252 * (0.45359237 * 9.80665) * 0.30480 * (1/60) / 745.6999 = 0.16 [dimensionless].

 

I haven't done a lot of research into the formula itself. If I needed this for work, some background might give me a clue what is going on. But I hope I have shown the problems challenges that an engineer faces daily.

 

 

No "s" in the acronym RPM, it stands for Revolutions Per Minute. Adding an s means Revolutions per minutes.

 

Your above statement is completely wrong. Two exactly the same objects being accelerated at different acceleration rates to the same final velocity will take a different amount of time to get to that velocity. The object that increases velocity at the greatest rate has the most POWER.

 

You're right about the RPM. In addition, adding the s would be confusing as people might take it for "second".

 

I don't see how I was (completely) wrong though when I said: "Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating.

Power is "energy per time" (J/s, or W), and energy input, as far as I am concerned, is the amount of energy you put into it (energy, in J (Joule)). I agree that the power is different, the energy is not... unless we're adding stuff like friction into the equation, which we shouldn't for now.

Edited September 12, 2008 by CaptainPanic

[traveler]

Here's a primer on where the 5252 comes from:

 

Torque is force times distance

 

1 HP=550 lb-ft of WORK per SECOND.

 

550 lb-ft of work per second for 60 seconds equals 33,000 lb-ft of WORK per MINUTE.

 

If you have a 1 lb load on the end of a 1 foot bar (1 lb-ft of TORQUE), and you rotate it 1 RPM, the load will travel 6.2832 feet (circumference of a 2 foot diameter circle) in one minute, which is 6.2832 lb-ft of WORK per MINUTE.

 

33,000 divided by 6.2832 equals 5252.

 

That means 1 lb-ft of torque at 5252 RPM is equal to 1 HP, OR HP=torque*RPM/5252.

 

That also means 6.2832 lb-ft of WORK per minute (1 lb-ft of torque at 1 RPM) divided by 33,000 equals .00019 HP

 

1 lb-ft of TORQUE times 1 RPM divided by 5252 equals .00019 HP

 

6.2832 lb-ft of WORK per MINUTE divided by 60 (seconds) equals .10477 lb-ft of work per SECOND.

 

Since 1 HP is 550 lb-ft of WORK per SECOND, .10477 divided by 550 equals .00019 HP

Edited September 12, 2008 by traveler

[CaptainPanic]

Nice illustration of the problem with non-SI units. You end up with a silly constant in your formula.

 

You can defend it whatever you want. But using SI units, all you need to do is derive the formula using only the symbols, and then fill it in using the SI units. Done. Never any discussion or mistake. Totally fool proof.

[traveler]

I don't see how I was (completely) wrong though when I said: "Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating.

Power is "energy per time" (J/s, or W), and energy input, as far as I am concerned, is the amount of energy you put into it (energy, in J (Joule)). I agree that the power is different, the energy is not... unless we're adding stuff like friction into the equation, which we shouldn't for now.

 

You are negating time.

 

If I accelerate 2 objects that are exactly the same, to a specific final velocity, the event is over when the one object accelerated at the greatest rate reaches the final velocity.

 

The object that accelerates at the greatest rate will achieve the final velocity in less time.

 

The other object will not even achieve the final velocity in the same time, so how can you say they both have the same energy? The race was to, say, 100 MPH. Let's say the object that had the greatest acceleration rate went from 0-100 MPH in 10 seconds. The other object was at a velocity of, say, 75 MPH at the 10 second mark, and did not travel as far in the same time. The event timer stops when the first object reaches 100 MPH. The timer doesn't keep going until the other object reaches 100 MPH! What was the faster object doing for that extended time? Did you also calculate that additional energy (per time) and consider that when you said the energy was the same? Not for the same time interval it wasn't.

Edited September 12, 2008 by traveler

[swansont]

That's changing the scenario, though. Two identical objects moving at the same speed have the same kinetic energy. Period. There was no "event timer" in the original formulation of the problem or in the statement about energy. That's a constraint that was added later.

[traveler]

That's changing the scenario, though. Two identical objects moving at the same speed have the same kinetic energy. Period. There was no "event timer" in the original formulation of the problem or in the statement about energy. That's a constraint that was added later.

 

Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating

 

Swansont, How can two objects moving at the same speed have different acceleration rates?

 

That is not what CaptainPanic said.

 

Please make a simple scenario such as mine to explain how two of the same objects can have different acceleration rates up to a similar speed (final velocity) and be traveling at the same speed?

 

Acceleration IS the rate of change of velocity. It doesn't occur "instantly," it takes time to accelerate!

Edited September 13, 2008 by traveler
multiple post merged

[swansont]

Swansont, How can two objects moving at the same speed have different acceleration rates?

 

 

v = at for constant a

 

 

Object 1 accelerates at 1 m/s^2 for 10 seconds. Object 2 accelerates at 2 m/s^2 for 5 seconds. They will both have a final speed of 10 m/s. There are an infinite number of ways it can happen.

[traveler]

v = at for constant a

 

 

Object 1 accelerates at 1 m/s^2 for 10 seconds. Object 2 accelerates at 2 m/s^2 for 5 seconds. They will both have a final speed of 10 m/s. There are an infinite number of ways it can happen.

 

What did object 2 do for the other 5 seconds?

[NeonBlack]

Nice illustration of the problem with non-CGS units. You end up with a silly constant in your formula.

 

[math]\epsilon_0[/math] is a rather silly constant isn't it?

 

Seriously though, the only silly thing here is arguing about unit systems. It is absolutely untrue that a scientist only uses SI units. I took a course last year where the only SI unit we used was the Kelvin. A scientist will use whatever units are convenient: electron-volt, parsec, angstrom, etc...

[swansont]

What did object 2 do for the other 5 seconds?

 

It was either at rest or moved at 10 m/s, depending on when the acceleration started.

[hobz]

Acceleration IS the rate of change of velocity. It doesn't occur "instantly," it takes time to accelerate!

I suppose you theoretically could come infintely close to an acceleration described by a (weighted) delta function.

 

Returning to the main question.

Suppose a satellite is told to move from A to B using a minimum amount of fuel.

Then why would it be most efficient, in terms of minimum fuel usage, to accelerate the satellite early on in stead of a constant acceleration?

[traveler]

It was either at rest or moved at 10 m/s, depending on when the acceleration started.

 

Rest=no acceleration

10 m/s=no acceleration (no change in velocity noted)

 

So, swansont, let's agree on the scenario first.

 

Let the two objects have an initial velocity of 0 m/s

 

Let the two objects accelerate for 10 seconds each, at different rates.

 

How far did each travel in 10 seconds if they both accelerated at different rates (10 m/s^2 and 5 m/s^2)?

 

 

Was the energy equal for the measured time?

 

Now, I know you are going to say time has nothing to do with it, so, I ask, how did you calculate the velocity without time? How did you know the velocity without measuring the actual meters traveled per time interval? No measurement means no known acceleration rate, so how do you know they are accelerating at 10 m/s^2 and 5 m/s^2, then?

 

Mass, distance, and time.

 

I suppose you theoretically could come infintely close to an acceleration described by a (weighted) delta function.

 

Returning to the main question.

Suppose a satellite is told to move from A to B using a minimum amount of fuel.

Then why would it be most efficient, in terms of minimum fuel usage, to accelerate the satellite early on in stead of a constant acceleration?

 

More power requires more fuel.

 

It takes more power to create the same force at a higher velocity (rotational or linear)

 

So at a higher velocity, to maintain the same force it requires more power, which requires more fuel.

Edited September 14, 2008 by traveler
multiple post merged

[swansont]

Rest=no acceleration

10 m/s=no acceleration (no change in velocity noted)

 

So, swansont, let's agree on the scenario first.

 

Let the two objects have an initial velocity of 0 m/s

 

Let the two objects accelerate for 10 seconds each, at different rates.

 

I don't agree. That scenario does not reflect the one described in the OP, where you can accelerate an object for up to 10 seconds, and both achieve the same final speed.

 

 

Was the energy equal for the measured time?

 

That doesn't matter. An object having 100 J of KE for 10 sec and another having 100 J of KE for 15 seconds still both have 100 J of KE.

[traveler]

Two identical objects accelerating (ideally) at different accelerations up to a similar speed (or: velocity) will both need exactly the same energy input, and will have the same kinetic energy when finished accelerating:

 

 

Swansont, What does this statement mean to you? This is what we are talking about, as you replied to earlier.

 

Are you trying to compare an apple to a orange?

 

Two identical objects moving at the same speed have the same kinetic energy. Period.

 

...and what do you mean by this statement?

 

Of course two of the same objects moving at the same speed have the same kinetic energy, but that doesn't say anything more than saying "an object's kinetic energy is the same as its kinetic energy." That's all you said.

 

Now explain with two different accelerations, like CaptainPanic's quote mentioned. ??

Edited September 14, 2008 by traveler
multiple post merged

[Bignose]

traveler.

 

Consider object A. It starts with an initial velocity of zero, and for 10 seconds accelerates at a rate of 1 m/s/s.

 

Consider object B, identical to A. It, too, starts with an initial velocity of zero, and for 10 seconds accelerates at a rate of (3/100)*t^2 where t is measured in seconds.

 

At 10 seconds, you know how fast both objects are going? Exactly 10 m/s.

 

This is the kind of thing swansont is talking about. Two identical objects that accelerate differently, but still end up the the same final speed will have the same KE. Period. As swansont mentioned, there are an infinite different number of way to doing this.

 

I think you are confusing the concepts of energy and power. Both energies will be same, but both powers will not, because power is rate of change of energy. Energy is simply the ability to do work, and both identical objects moving at identical speeds have the same ability to do work -- or completely equivalently have had the same amount of work performed on them. Energy says nothing at all about how fast or slow that work was applied. That is what the concept of power was invented for.

[swansont]

Swansont, What does this statement mean to you? This is what we are talking about, as you replied to earlier.

 

Are you trying to compare an apple to a orange?

 

 

 

...and what do you mean by this statement?

 

Of course two of the same objects moving at the same speed have the same kinetic energy, but that doesn't say anything more than saying "an object's kinetic energy is the same as its kinetic energy." That's all you said.

 

Now explain with two different accelerations, like CaptainPanic's quote mentioned. ??

 

Two different accelerations that leave you with the same final speed.

 

The question is what is your interpretation of the statement? You seem to be envisioning a different scenario than is laid out by the OP.

[traveler]

traveler.

 

Consider object A. It starts with an initial velocity of zero, and for 10 seconds accelerates at a rate of 1 m/s/s.

 

Consider object B, identical to A. It, too, starts with an initial velocity of zero, and for 10 seconds accelerates at a rate of (3/100)*t^2 where t is measured in seconds.

 

At 10 seconds, you know how fast both objects are going? Exactly 10 m/s.

 

This is the kind of thing swansont is talking about. Two identical objects that accelerate differently, but still end up the the same final speed will have the same KE. Period. As swansont mentioned, there are an infinite different number of way to doing this.

 

I think you are confusing the concepts of energy and power. Both energies will be same, but both powers will not, because power is rate of change of energy. Energy is simply the ability to do work, and both identical objects moving at identical speeds have the same ability to do work -- or completely equivalently have had the same amount of work performed on them. Energy says nothing at all about how fast or slow that work was applied. That is what the concept of power was invented for.

 

Can you give an example of work getting done in zero time? How about accelerating an object in zero time? How about a measure of velocity in zero time?

 

DO NOT NEGATE TIME.

 

The equations are made to calculate actual measurements of mass, distance, and time (motion). Mass, distance and time IS motion. The math is to describe reality, not the other way around.

 

Two different accelerations that leave you with the same final speed.

 

The question is what is your interpretation of the statement? You seem to be envisioning a different scenario than is laid out by the OP.

 

Please answer my previous questions. I made my point earlier.

Edited September 14, 2008 by traveler
multiple post merged

[Bignose]

Can you give an example of work getting done in zero time? How about accelerating an object in zero time? How about a measure of velocity in zero time?

 

DO NOT NEGATE TIME.

 

The equations are made to calculate actual measurements of mass, distance, and time (motion). Mass, distance and time IS motion. The math is to describe reality, not the other way around.

 

 

You are confusing mathematics and reality -- they don't necessarily have to coincide. It is exceptionally common to approximate reality with mathematical structures that don't occur in reality.

 

To borrow an example from a different thread. When launching a probe to Mars from Earth, the gravitational effect of Pluto is considered. But, in the mathematical models, Pluto is treated as a point source of mass. That is, the variations in density across the volume of Pluto aren't important -- treating Pluto as a point source of mass is accurate enough. Is Pluto a point source of mass in reality? Of course not -- nothing is. That doesn't stop us from modeling it as a point source.

 

As other example, many, many times we model objects as spheres. But, there is no such thing as a perfect sphere. In most of the situations, treating the object as a sphere introduces so little error that it is more than good enough to approximate it that way.

 

Sure, things in reality do take time. But, lots of things accelerate very quickly. When Tiger Woods stands on the tee and hits a golf ball with his driver the golf ball accelerates from 0 mph to over 150 mph in just a tiny, tiny amount of time. 0.0005s is how long a golf ball remains on the face of a golf club. Treating that ball as instantaneously achieving its velocity isn't that bad of an approximation. Especially if you are doing something like modeling the entire flight of the ball that will take something like 5 to 8 seconds of total flight time. 0.0005 one way or the other doesn't really change the final modeled result.

 

Finally. What does this have to do with your original question/issue anyway? I showed you an example of two objects that accelerate at different rates but still end up with the same velocity.

 

You want another one that will start at zero acceleration at zero time? Fine: How about object C that accelerates at (1/250)t^3 m/s/s where t is measured in seconds. At 10 seconds, it too will have a velocity of 10 m/s. Another? object D accelerates at (1/20000)t^4 m/s/s again where t is measured in seconds. It too will have a velocity of 10 m/s after 10 seconds of acceleration.

 

I can keep doing this, I can come up with an infinite number of different ways of accelerating an object so that after 10 seconds they all have the same velocity.

 

This isn't that hard to do, even putting in the constraints you are complaining about. Even if you dismiss object A because it instantly starts accelerating, object B,C, and D all have zero acceleration at time zero and take time to build up acceleration.

 

And, since they all have had the same amount of work done on them at t=10 seconds, they all have the same energy.

 

Again, the total amount of work has nothing to do with at what rate that work was applied. That's the concept of power.

 

Let me give you a farcical example. Let's say you open a bank account. After 4 weeks, you have $1000 in it. Does is matter if you were paid $250 a week or $500 every two weeks or $1000 a month? No, because at the end of the month, you have $1000 in it.

 

It is the same way with energy. An object has a certain amount of energy -- or equivalently a certain amount of work has been performed on it -- it doesn't matter if it was applied continuously or in bursts. In the end, it has a fixes amount of work. The rate of work -- the power (analogous to the rate at which you get paid) can be different. But in the end, you have the same amount. End of story.

[swansont]

Please answer my previous questions. I made my point earlier.

 

This one?

Swansont, How can two objects moving at the same speed have different acceleration rates?

 

They don't accelerate for the same length of time, or their acceleration is not a constant (i.e. it's a function of time)

 

(If you are referring to questions in post #18, I'm not going to address them as they are off-topic.)