Unlimited Revs & Gears: Top Speed Possibilities

In summary, if you had an engine that had unlimited revs or gears, it would have infinite top speed, but air resistance and the universal speed limit would affect it.
  • #1
fedorfan
115
0
Hypothetically, if you had an engine that had unlimited revs or unlimited gears would it have infinite top speed NOT acknowledging air resistance,universal speed limit, and fuel?
 
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  • #2
fedorfan said:
Hypothetically, if you had an engine that had unlimited revs or unlimited gears would it have infinite top speed NOT acknowledging air resistance,universal speed limit, and fuel?
No, it would never reach the speed of light.
 
  • #3
fedorfan, if you throw enough rediculous hypotheticals into a question you can get any answer you want. But the answer isn't terribly useful.
 
  • #4
According to Newton's laws of mechanics, it could have infinite top speed. But according to Einstein, it could not.

Experiments show that Einstein is more nearly right that Newton was.
 
  • #5
Why wouldn't it? If it has unlimited gears doesn't that mean it would accelerate forever? I know its a pointless question but I was just wondering.
 
  • #6
fedorfan said:
Why wouldn't it? If it has unlimited gears doesn't that mean it would accelerate forever? I know its a pointless question but I was just wondering.

That doesn't follow, even for Newtonian mechanics.

Suppose the acceleration is [tex]e^{-t}[/tex] and the initial velocity is 0. The velocity at time t is [tex]1-e^{-t}[/tex]. The accleration is always positive, but the velocity is always less than 1.
 
  • #7
To expand on AlephZero's mention of Einsteinian physics:

The faster something moves, the more kinetic energy it has. E=mc^2, so the faster it moves, the heavier it becomes. The heavier it becomes, the greater force is required to accelerate it more. If that is possible, then it becomes faster and hence heavier again. As you can see, it's just a vicious cycle, meaning that the acceleration will approach zero and hence velocity will approach a certain value, which in our universe is the speed of light, c.

That's the explanation in a nutshell. For more information look up special relativity.
 
  • #8
fedorfan said:
Why wouldn't it? If it has unlimited gears doesn't that mean it would accelerate forever? I know its a pointless question but I was just wondering.
It is not really a pointless question at all. There are motor designs that can do this in principle. Look up 'Bussard ramjets'.

Anyway, it will accelerate forever, yes, but as per Einstein's Special Theory of Relativity, a constant acceleration doesn't result in a constant increase in velocity.

Here is a chart of acceleration vs. velocity over a fixed timeframe. Say your engine can accelerate your craft to 90% of c over the course of one year (a constant acceleration of a).

Code:
Time Elapsed    Acceleration   Velocity (as a per cent of c)
0 (Start)            a                   0
after one year       a                  90
after two years      a                  99
after three years    a                  99.9
after four years     a                  99.99
after five years     a                  99.999
...
I've just ballparked the numbers, but they are easily calc'ed.
 
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  • #9
DaveC426913 said:
but as per Einstein's Special Theory of Relativity, a constant acceleration doesn't result in a constant increase in velocity.

Hi DaveC, I may be nitpicking here, but when I studied special relativity back in high school, I had a lot of trouble with statements such as this one, because it doesn't specify the frame of reference from which you're viewing the body. I feel it's important to specify that here, "constant acceleration" is the "apparent acceleration" from the point of view of someone who is, say, riding on the engine.

This link explains it more clearly than I do. http://physics.nmt.edu/~raymond/classes/ph13xbook/node59.html" [Broken]
 
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  • #10
electricsheep said:
Hi DaveC, I may be nitpicking here, but when I studied special relativity back in high school, I had a lot of trouble with statements such as this one, because it doesn't specify the frame of reference from which you're viewing the body. I feel it's important to specify that here, "constant acceleration" is the "apparent acceleration" from the point of view of someone who is, say, riding on the engine.

This link explains it more clearly than I do. http://physics.nmt.edu/~raymond/classes/ph13xbook/node59.html" [Broken]

Agreed. But I thought that a fairly simple question could be given a simple answer without overdoing it.
 
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  • #11
fedorfan said:
Hypothetically, if you had an engine that had unlimited revs or unlimited gears would it have infinite top speed NOT acknowledging air resistance,universal speed limit, and fuel?

No. It could not have infinite top speed. Not even hypothetically. If it could, it would not move at all and be where it was going.
 
  • #12
Alright, I see what yall are saying here, that the faster you go the heavier you get. Oh, and I didnt mean infinite top speed that way, I meant it wouldn't stop accelerating. That bussard ramjet is very interesting and an ingenious but simple idea. Why haven't they made one yet?
 
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  • #13
fedorfan said:
That bussard ramjet is very interesting and an ingenious but simple idea. Why haven't they made one yet?
Lot of info out there about it - it's been studied. The technology is far beyond current ability.
 
  • #14
If both were working to their full capabilities, which one would be faster, an annihilation engine or a bussard ramjet?
 
  • #15
electricsheep said:
The faster something moves, the more kinetic energy it has. E=mc^2, so the faster it moves, the heavier it becomes...
This is an adequate explanation in the light of the question asked, but one should note that E=mc^2 refers to the rest energy of an object, which stays constant under acceleration by an external force.

It is really the relativistic momentum that increases with speed and approaches infinity in any inertial reference frame if the speed in that frame approaches the speed of light. The relativistic momentum is given by:

[tex]p = \frac{mv^2}{\sqrt{1-v^2/c^2}}[/tex]
 
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  • #16
Jorrie said:
This is an adequate explanation in the light of the question asked, but one should note that E=mc^2 refers to the rest energy of an object...

Actually, I don't think E is the rest energy, because that would imply m is the rest mass, which is not incorrect but entirely irrelevant to what I was explaining there. I'm fairly sure E is properly defined as the "mass energy", which is just the amount of energy equivalent to a certain mass. In our case of accelerating a body, this "mass energy" originates from an increase in kinetic energy. Everything I've (quickly) found online so far doesn't contradict what I said. Please provide me with a reference if I'm wrong.

Jorrie said:
It is really the relativistic momentum that increases with speed and approaches infinity in any inertial reference frame if the speed in that frame approaches the speed of light. The relativistic momentum is given by:

[tex]p = \frac{mv^2}{\sqrt{1-v^2/c^2}}[/tex]

You've lost me there. You seem to be saying that if the speed increases, then the relativistic momentum increases. I agree but that's nothing to do with our discussion. And your expression is also incorrect. It should be:
[tex]p = \frac{{m_0}v}{\sqrt{1-v^2/c^2}}[/tex]
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c1"
 
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  • #17
The new definition of mass

electricsheep said:
Actually, I don't think E is the rest energy, because that would imply m is the rest mass, which is not incorrect but entirely irrelevant to what I was explaining there...
Please provide me with a reference if I'm wrong.
You are not wrong, just the modern concept of mass is different. See
http://www.geocities.com/physics_world/mass_paper.pdf

If you search the relativity forum on this, you will also find lots of discussion on it.
electricsheep said:
And your expression is also incorrect. It should be:
[tex]p = \frac{{m_0}v}{\sqrt{1-v^2/c^2}}[/tex]
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/relmom.html#c1"
This is the "older" definition. The use of the terms rest mass and relativistics mass is on the decline, but still found in plenty of writings, making it somewhat confusing sometimes.

Also, the total relativistic energy is lately given by: [tex]E = \frac{mc^2}{\sqrt{1-v^2/c^2}}[/tex], where [tex]m[/tex] is the proper mass, or rest mass, or just mass...
 
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  • #18
Jorrie said:
You are not wrong, just the modern concept of mass is different. See
http://www.geocities.com/physics_world/mass_paper.pdf

Nice.

Jorrie said:
This is the "older" definition. The use of the terms rest mass and relativistics mass is on the decline, but still found in plenty of writings, making it somewhat confusing sometimes.

That wasn't what I was trying to point out. Your original expression for relativistic momentum had [tex]v^2[/tex], which made me do a double take and do a quick search on the web just to confirm my memory. But yes, I think I'm thread-jacking now. My apologies.
 
  • #19
Oops

electricsheep said:
That wasn't what I was trying to point out. Your original expression for relativistic momentum had [tex]v^2[/tex], which made me do a double take and do a quick search on the web just to confirm my memory. But yes, I think I'm thread-jacking now. My apologies.

Oops! I'm sorry for having missed that [tex]v^2[/tex] - it's surely wrong in momentum!

I think to conclude this "diversion" (started by me), it is better to work with relativistic total energy that diverges to infinity as an object nears the speed of light than to work with relativistic mass that diverges. But, in the end, it is a matter of choice, I guess.
 

1. What is "Unlimited Revs & Gears" and how does it work?

"Unlimited Revs & Gears" is a feature in some high-performance vehicles that allows the engine to rev higher and shift into higher gears at a faster rate. This is achieved through advanced engine tuning and transmission technology, allowing for faster acceleration and higher top speeds.

2. Is "Unlimited Revs & Gears" safe for the engine and transmission?

In most cases, "Unlimited Revs & Gears" is safe for the engine and transmission as long as the vehicle is properly maintained and not pushed beyond its limits. However, constant use of this feature may result in increased wear and tear on the engine and transmission.

3. What are the benefits of "Unlimited Revs & Gears"?

The main benefit of "Unlimited Revs & Gears" is improved performance and speed. It allows for faster acceleration and higher top speeds, making it ideal for racing or track use. It can also provide a more exhilarating driving experience for those who enjoy high-speed driving.

4. Can "Unlimited Revs & Gears" be added to any vehicle?

No, "Unlimited Revs & Gears" is typically only available in high-performance vehicles that are specifically designed for racing or track use. It requires advanced engine and transmission technology that is not commonly found in regular consumer vehicles.

5. Are there any downsides to using "Unlimited Revs & Gears"?

While "Unlimited Revs & Gears" can provide improved performance, it also has some downsides. It may result in decreased fuel efficiency and increased wear and tear on the engine and transmission. It also requires proper training and skill to use effectively, as pushing the vehicle beyond its limits can be dangerous.

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