TNGTM pg 55 Warp Factor vs Power chart equation

[feld]

Folks,

I’m terribly sorry because I am certain tech fandom knows this but I cannot seem to find it. i would greatly appreciate it if anyone could point me to the math behind the well known “sawtooth” warp factor power consumption graph on pg 55 of the venerable Star Trek The Next Generation Technical Manual.

Note I’m not looking for the well established warp factor vs Cochranes (speed of light multiple) but the sawtooth shaped power graph

Apologies that my Google fu has failed me. I’ve found old posts on this board that duplicate the chart and have their own approximations to it but I wondered if Mr. Sternbach or Mr Okuda ever just posted the equations…

Thanks in advance for any help you can provide.

 

[Kamen Rider Blade]

Spoiler: The TNG:TM Power Consumption : Warp Factor Chart

Yes, I marked it up for my own purposes of measuring where things are.
Too my knowledge there was no formula for the power consumption side relative to Warp Factor.

Spoiler: TNG:TM Manual Power Consumption : Warp Factor in nicer format.

As you can tell, power consumption spikes dramatically as you approach each Warp Factor Threshold before it slides down a bit.
But the over-all power consumption increases is pretty drastic with each Warp Factor IMO.

Spoiler: TNG:TM Power Consumption relative to Warp Factor using my Warp Factor Scale 3.0

The only difference between my Warp Factor Scale & the TNG-era one was that I ignore the hand drawn curve to infinity after Warp Factor 9 and naturally used the TNG era formula and let it run on naturally to infinity.
I've discovered that almost all practical use cases in show could be easily explained with Warp Factor 1.0 - 1000.0, anything faster than that will be too fast.

No need for Wf 9.999… until infinite 9's needs to be mentioned, natural numbers can be easily uttered by actors instead of mentioning how many 9's after the decimal seperator.
It's a far simpler system with no BS hand-drawn curve to infinity after Warp Factor 9.0.

Spoiler: Warp Factor to Power consumption curve in ST:ENT

Here it is used in ST:ENT

 

[knightgrace]

AND what little that I can add, is that warp factors are treated in TNG, in particular as the gears in an automatic nine speed transmission in your car...

Which raises another question...

What would a one speed transmission mission for a starship be like? Remember that this is a metaphor. What it means is that as you approach the next gear shif, the amount of power to get to the next gear(warp factor), will drop...in a car or bus, by about six hundred rpm. In a semi, this occurs at about 1,650 rpm... in a bus, about 2,200 to 2,400 rpm.

Keep in mind that a semi today has 13 to 18 speed transmissions.


One of the possible issues is that a Shuttlecraft might have a two speed, covering from 1c to...let's say 3053c+.

A small actual ship, might have a a six speed transmission covering from 1c to 3053c+.

The Enterprise-D, being so massive requires a nine speed.

Keeping further in mind that the highest gear handles all speeds above a certain x light speed. My car, reaches sixth gear around forty miles per hour. The semi that I drove reached eight high at 55 miles per hour. But cars top out around forty...why?

Because of the lack of load. Which means that two speed is valid.

 

[feld]

Spoiler: The TNG:TM Power Consumption : Warp Factor Chart

Yes, I marked it up for my own purposes of measuring where things are.
Too my knowledge there was no formula for the power consumption side relative to Warp Factor.

As you can tell, power consumption spikes dramatically as you approach each Warp Factor Threshold before it slides down a bit.
But the over-all power consumption increases is pretty drastic with each Warp Factor IMO.

The only difference between my Warp Factor Scale & the TNG-era one was that I ignore the hand drawn curve to infinity after Warp Factor 9 and naturally used the TNG era formula and let it run on naturally to infinity.
I've discovered that almost all practical use cases in show could be easily explained with Warp Factor 1.0 - 1000.0, anything faster than that will be too fast.

No need for Wf 9.999… until infinite 9's needs to be mentioned, natural numbers can be easily uttered by actors instead of mentioning how many 9's after the decimal seperator.
It's a far simpler system with no BS hand-drawn curve to infinity after Warp Factor 9.0.

Spoiler: Warp Factor to Power consumption curve in ST:ENT

Here it is used in ST:ENT

Ok thank you. Yours was the main post I found on this topic. Did you fit the power per cochrane curve using a least squares or something? Or just pick off enough points to reproduce it for your own use? Only reason I bring it up is that the out of universe note in the TM on the same page mentions Mr. Okuda using a Excel spreadsheet to get “speeds and times” and I wondered if they’d made some kind of crazy function for the power as well.

If you haven’t already (who am I kidding…everyone else in Trek tech fandom has probably done this before me) go back calculate how much antimatter it’d take to do warp six for three years. If I did my math right you’ll find that it’s pretty close to the TM’s 3000 m3 antimatter tankage for a Galaxy class…which they state lasts for a “standard mission duration” of three years. I assumed slush antideuterium had twice the density of slush hydrogen (I used 170 kg/m3). That implies the authors did that math.

I work in aerospace and am continually impressed by some of the details in this book. Have been increasingly so for 34 years.

Of course…given that this all holds together…with a few assumptions we can calculate time to fuel exhaustion for a Galaxy for any warp factor profile…always acknowledging that warp factors are less a measure of how fast you’re going and more a measure of how hard you’re pushing…like a ship’s turns per knot ratio on its propellers. It doesn’t mention how hard space pushes back…

Given a few MORE assumptions you could estimate hotel load, how much combat time the ship would have left, how many fully loaded photorps she could fuel…lotsa stuff.

And if you really wanted to go nuts you could do this for any ship by assuming some relationships between starship mass and or volume and the power per cochrane…

Yeah…this way madness lies…but I like this kind of madness…

 

[Kamen Rider Blade]

Ok thank you. Yours was the main post I found on this topic. Did you fit the power per cochrane curve using a least squares or something?

No, I didn't go that far.

Or just pick off enough points to reproduce it for your own use?

I just wanted to see what part of the Warp Factor Scale did the Power Consumption Curve start increasing drastically and it was close to the half way points between Whole Number Warp Factors.
After that, it seemed to fall off back to the original slope.

Only reason I bring it up is that the out of universe note in the TM on the same page mentions Mr. Okuda using a Excel spreadsheet to get “speeds and times” and I wondered if they’d made some kind of crazy function for the power as well.

I never found any formula within the TNG:TM for the power consumption, I'm assuming it's a "hand-drawn curve" just like the "hand-drawn curve" to Infinity after Warp Factor 9.0 in the TNG era formula which is silly & non-sensical IMO.

If you haven’t already (who am I kidding…everyone else in Trek tech fandom has probably done this before me) go back calculate how much antimatter it’d take to do warp six for three years.

Actually I haven't done that, so if you could do it, be my guest.

If I did my math right you’ll find that it’s pretty close to the TM’s 3000 m3 antimatter tankage for a Galaxy class…which they state lasts for a “standard mission duration” of three years. I assumed slush antideuterium had twice the density of slush hydrogen (I used 170 kg/m3). That implies the authors did that math.

Interesting. I'd love to see your calculations and work for that if you don't mind.
What Cruise Speed did you use for the Galaxy Class?
Memory Alpha only lists a intial Cruise Speed of Wf 6.0

I work in aerospace and am continually impressed by some of the details in this book. Have been increasingly so for 34 years.

What part of AeroSpace do you work in?

The TNG:TM along with all it's details was designed by those who had a similar mentality.
Design a vessel that's plausible given it's technological capabilities within the storyline universe.