Time - Acceleration - Distance (and Velocity)

[Bartman]

Years ago at the request of another poster, I cobbled together a quick calculator where in if you had two of the variable (T, A or D) you would get the third. Very useful for 'hard'ish sci-fi. How long does it take to get to the moon? Simply enter the distance, and acceleration in Gs (or fractions there of) and voila.

 

Well I updated the file last year and realized I had never reposted it. So here it is. TAD 2.0. It is a Excel 2000 spreadsheet. Simply enter the variables you know to get the one you don't. TAD 2.0 has improved values for some of the constants, a nicer look and feel, and corrected at least one horrendous math mistake.

 

Just one thing to remember though. Everything assumes constant linear acceleration. If your PCs intend to stop at the end of the trip they better have really good brakes. Otherwise you should remember set your distance to half of what you want, and then double the time (acelerate for half the distance and decelerate the other half).

[Steve Long]

Re: Time - Acceleration - Distance (and Velocity)

 

Sounds cool -- have to give it a try next time I plan a trip to Mars!

[Nyrath]

Re: Time - Acceleration - Distance (and Velocity)

 

A "Brachistochrone" mission is where you accelerate constantly to the midpoint, flip over ("skew flip"), and decelerate to the destination.

 

I'm sure you could easily add it to your spreadsheet, the formula is:

T = 2 * sqrt[ D/A ]

 

If you wish to learn more than you want to know about such matters, read about it here on my web site.

[Basil]

Re: Time - Acceleration - Distance (and Velocity)

 

Years ago at the request of another poster, I cobbled together a quick calculator where in if you had two of the variable (T, A or D) you would get the third. Very useful for 'hard'ish sci-fi. How long does it take to get to the moon? Simply enter the distance, and acceleration in Gs (or fractions there of) and voila.

 

Well I updated the file last year and realized I had never reposted it. So here it is. TAD 2.0. It is a Excel 2000 spreadsheet.

 

I don't have anything that can use an Excel document, but no worries.

 

There are four variables: time (T), distance (D), acceleration (A), and instantanious velocity (V). Given any two (in seconds, meters, m/s/s and m/s repectively), you can find the other two.

 

The formulae (grouped by which you want to find) are:

V = AT = (2AD)^.5 = 2D/T

A = V/T = V^2/(2D) = 2D/(T^2)

T = V/A = 2D/V = (2D/A)^.5

D = (V^2)/(2A) = (VT)/2 = (A(T^2))/2

 

BTW, this assumes constant acceleration in one direction, with no "outside" forces.