Distance traveled given acceleration?

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Discussion Overview

The discussion revolves around comparing the distance traveled by a full-sized car and a remote-controlled (RC) car given their acceleration and time to reach a specific speed (0-60 mph). Participants explore the implications of vehicle specifications, scaling factors, and the nature of acceleration in different types of vehicles.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants suggest that if both vehicles have identical acceleration profiles, they would travel the same distance, but this is contingent on the nature of their acceleration.
  • Others argue that acceleration is not constant for vehicles, particularly between electric and internal combustion engines, which complicates the comparison.
  • A participant proposes measuring acceleration over time for both vehicles to obtain more accurate data rather than relying solely on specifications.
  • One participant expresses a desire to create a "true scale" model for the RC car, questioning how to accurately scale speed and performance from the RC to a full-sized vehicle.
  • There is discussion about the implications of scaling factors, such as weight and power, and how they do not scale linearly, which could affect performance comparisons.
  • Another participant calculates the distance traveled by the RC car using a scale speed converter, leading to a debate about the validity of the results and the assumptions made in the calculations.
  • Some participants highlight that the scaling of mass and power does not follow the same ratio as the dimensions of the vehicles, impacting acceleration and performance.
  • There is a mathematical expression provided to relate acceleration, time, and distance, but its applicability remains uncertain among participants.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether the same acceleration leads to the same distance traveled, as many factors, including vehicle type and scaling, introduce complexity and uncertainty into the discussion.

Contextual Notes

Participants note that assumptions about constant acceleration and scaling may not hold true across different vehicle types, and the discussion includes various calculations and interpretations that are not universally accepted.

Who May Find This Useful

This discussion may be of interest to those exploring vehicle dynamics, scaling laws in modeling, and the physics of acceleration in different types of vehicles.

gordonlingley
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I have what I'm assuming is a pretty simple question:

I'm trying to compare the distance traveled by two vehicles given a time and acceleration. Specifically, I'm comparing a full-sized car (196" in length) that goes 0-60mph in roughly 3 seconds vs. a remote controlled car (27" in length) that features roughly the same acceleration? Do they both travel the same distance? Do I need to take into account an vehicle specifics, such as the length of the car or the circumference of the tires?

Thanks.
 
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If the acceleration versus time is identical for both vehicles, then they travel the same distance. However, even if both of them accelerate from 0 to 60 mph in 3 seconds, if one of them accelerates quicker for 0 to 40 mph, then slower for 40 mph to 60mph, so it ends up 0 to 60 mph in 3 seconds, then the distance will be longer (more time spent above 40 mph than the other vehicle).
 
Your problem here is that things don't scale as simply as you would like. This is particularly true if your model is electric and your full size is Internal Combustion. When a car goes from 0 to 60, the acceleration is far from constant (see the above post) because of engine characteristics and gear changes. If you could actually measure the acceleration over time (say with an IPhone App) for the car and the model, you might get some interesting graphical results. (Some good padding could be useful in the model car, in case of an accident.
gordonlingley said:
Do I need to take into account an vehicle specifics, such as the length of the car or the circumference of the tires?
That would depend on what you actually want to find out. If you wanted to produce a 'true scale' model of speed over distance performance then you may find the easiest way could be to take your real car, see how far it travels when accelerating flat out and then do a number of runs of the model car over a scaled distance, using a range of power settings until it actually travels the required scale distance in your 3 seconds.
 
To see how far they run, of course you should take their velocity into account. The same acceleration can imply few information of velocity, which just reveals their same changing rate to the time.
 
Here's a little more context which might shed more light on the subject...

I'm trying to compare a Tesla P85D, which can apparently do 0-60mph in 2.8 seconds vs. a 1/7 scale Traxxas XO-1 electric RC car, which can apparently do 0-60 in an astonishing 2.3 seconds. Since both are electric vehicles, can I assume, for these rough purposes, that acceleration is basically constant (or at least close enough)?

sohiecentaur - I would definitely like to figure out a "true scale" model for the RC car as well. The RC car is 1/7 scale. Is there some sort of equation that will help me figure out the "if the car was full-sized, how fast is it actually going question?" My naive gut would love to believe that, if everything scaled accordingly (power, weight, etc.) the full-sized RC car would be able to do the 0-60 in a ridiculous 0.32 seconds. But my gut is also telling me that I'm probably wrong.

Unfortunately, I don't actually have physical access to either of these vehicles, I'm merely basing my equations off of the specs listed on the respective websites.

Some more info that will either confuse or clarify things furthur:
The RC car has a 1650 kV electric motor. I found an online conversion calculator that put this at roughly 2212 hp. Is that correct/possible? If I scaled everything with my previously demonstrated naive assumptions, that would put the kV at 11,550 and the hp at 15,488. At which point the numbers are getting so large I feel I must be doing something (many things) wrong. Also, the RC car weighs in at a modest 10.3 lbs. I'm guessing it's not accurate to assume that a full-scale model will only weigh 72.1 lbs. (vs. the Tesla's 4,830 lbs.)

Now that you all know the comparison I'm trying to make, what information do I need to make the comparison as accurate as possible?

Thanks.
 
gordonlingley said:
The RC car has a 1650 kV electric motor.
The Kv rating is no load rpm versus voltage, in this case, 1650 rpm per volt. Wiki article:

http://en.wikipedia.org/wiki/Motor_constants#Motor_velocity_constant.2C_back_EMF_constant

A typical RC motor's torque is greatest at 0 (stall) rpm, and decreases linearly to zero as it reaches maximum rpm. This would mean the acceleration of the RC car is greatest at the start and decreases as speed increases, even ignoring other losses like internal friction, aerodynamic drag, ... .
 
Ah. Awesome. That makes more sense.
 
Okay, I found this website: http://webpages.charter.net/sinkwich/sdventure/html/sd_scale_speed.htm

It has a scale speed converter. Given the time, 2.3 seconds, and the final velocity, 60mph, I was able to determine what I believe to be the distance traveled, roughly 2,429 inches. Using the converter, it gave me the following scaled speed of roughly 420mph... which seems too easy an answer... since it's basically just the 60mph multiplied by 7 for the scaling. However, if that's accurate, I could live with it.

Does anybody agree with this finding? Or dispute it?

Thanks.
 
gordonlingley said:
sohiecentaur - I would definitely like to figure out a "true scale" model for the RC car as well. The RC car is 1/7 scale. Is there some sort of equation that will help me figure out the "if the car was full-sized, how fast is it actually going question?" My naive gut would love to believe that, if everything scaled accordingly (power, weight, etc.) the full-sized RC car would be able to do the 0-60 in a ridiculous 0.32 seconds. But my gut is also telling me that I'm probably wrong.

Your gut is indeed correct. Different aspects of the car do not scale the same way. For example, the car is a 1/7th scale model, which means that all the dimensions are reduced to 1/7th of normal. However, the mass is scaled down MUCH more than 1/7th. The model is 4.67 kg with batteries.The Tesla P85D has a mass of right around 2268 kg. So the mass of the model is scaled down to 1/485th of normal. This has a drastic impact on multiple aspects of the car, especially acceleration. The motors scale similarly. They increase in mass MUCH faster than they increase in power. So if you try to scale up the model, you wind up with performance at least vaguely comparable to the Tesla P85D.
 
  • #10
I dispute it. Not sure how to work that calculator.
I calculate 1214 inches assuming constant acceleration from 0 to 60.
 
  • #11
gordonlingley said:
Okay, I found this website: http://webpages.charter.net/sinkwich/sdventure/html/sd_scale_speed.htm

It has a scale speed converter. Given the time, 2.3 seconds, and the final velocity, 60mph, I was able to determine what I believe to be the distance traveled, roughly 2,429 inches. Using the converter, it gave me the following scaled speed of roughly 420mph... which seems too easy an answer... since it's basically just the 60mph multiplied by 7 for the scaling. However, if that's accurate, I could live with it.

Does anybody agree with this finding? Or dispute it?

Thanks.

All that converter does is tell you that if a 1/7th scale model moves X inches over time, then the scaled up velocity is 7X/T. When you put in your velocity as 60 mph, the calculate automatically found the distance the model traveled in inches per 2.3 seconds. Then it just multiplied this by 7 and found the new scaled up velocity. It doesn't tell you anything about acceleration, as it assumes a constant velocity.
 
  • #12
Consider
a = delta v/ delta t
where delta's are finit then
S = delta v * delta t =
a * (delta t)^2
So it seems for a moment.
 
  • #13
You don't need any scaling for this.
IF they have the same acceleration, they both start from rest and they move for the same duration the distance traveled will be the same. It does not depend on the size, mass or shape of the objects.

But this is a big "IF".
Even if you know that both go form 0 to 60 in the same time, you can only say that they have the same average acceleration. The distance traveled cannot be found from just average acceleration. You have to know how the acceleration varies with time. So you cannot tell if they do or not travel the same distance from just the information given.
Again, scale is irrelevant. Even if you have two cars with same mass and size, and they both go from 0 to 60 in the same time, it would be possible that they travel different distances.
 
  • #14
nasu said:
You don't need any scaling for this.
But I thought the whole thread was about scale models with correct scale speeds and accelerations?
(I could be wrong, of course)
 
  • #15
It was deviated into this.
The OP mentioned that he wants to compare the distances traveled by two cars with the same average acceleration.
Because one of them is a model it was somehow assumed that scaling has something to do with it.
 
  • #16
nasu said:
It was deviated into this.
The OP mentioned that he wants to compare the distances traveled by two cars with the same average acceleration.
Because one of them is a model it was somehow assumed that scaling has something to do with it.
That's a daft notion. By that reckoning, a big car would go faster and further than a small car.
 
  • #17
No, it wont. IF they have the same acceleration (at all times, not just average) they will go the same distance. And will have the same speed.
Once we have the acceleration, it's all kinematics. The mass of the car does not matter.
The question (originally) was not about dynamics, about which one will have more power etc.
He explicitly said
"that features roughly the same acceleration".
Of course you will need more force to get the same acceleration on the real car and scaling will be important to figure out HOW to satisfy this condition.
But once the same acceleration is assumed, it is all kinematics.
 
  • #18
Yet again a PF thread goes in circles. :biggrin:
 
  • #19
Or maybe just loops. :wink: :smile:
 
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