Physics of Orville vs. Enterprise

In The Orville episode, "Pria," we learn that the ship can travel upwards of ten lightyears (ly) an hour. Like the warp factor scale used in Star Trek, this is a measure of a ship's speed. To determine which ships are faster, whether the Orville is faster than any of the ships that have borne the name Enterprise, we need to convert the units into a form we can compare. For the sake of ease and convenience, we will compare everything relative to the speed of light, c.

The Orville's Speed

We will assume that the 10 ly hr-1 is the ship's maximum speed and that it can go faster in emergency situations. While this unit is more intuitive than Star Trek's warp factor, we still don't have a sense of what it actually means. We know the ship can travel faster than the speed of light but we can't say by how much.

A light year is the distance a beam of light travels in one year. We can race the Orville with a beam of light and compare distances to see how much faster the ship is, or we can work out the maths. There are 8,760 hours in a year. We can figure out the distance (d) by multiplying the speed (v) with time (t).

d = v \times t


So if the Orville was to run its engines for an entire year, it would travel a distance of

d=10 \times 8760 = 87,600 \text{ ly}


In one year, the Orville travels 87,600 times the distance a beam of light does. Another way of looking at this is the Orville travels 87,600 faster than the speed of light or 87,600c.

v = 87,600c

Enterprise NX-01 Speed

The Enterprise NX-01

The maximum warp speed of the NX-01 is 5.06. We can determine the speed from the formula

v = w^{3}c


where v is the speed, w is the ship's warp factor, and c is the speed of light. Substituting the NX-01's maximum warp into the equation, we get

v = (5.06)^{3}c=127.26c


Under emergency conditions, we substitute 5.2 into the equation and get

v = (5.2)^{3}c=140.61c

USS Enterprise NCC-1701 Speed

The USS Enterprise NCC-1701

The maximum warp speed of the NCC-1701 is 8.0. Substituting this into the equation and we get

v=(8.0)^{3}c=512c

USS Enterprise NCC-1701D

USS Enterprise NCC-1701D

The warp formula changed with Star Trek: The Next Generation to

v=w^{\frac{10}{3}}c


This only applies for the interval between warps 1 to 9. For warp values beyond nine, speed is derived from a hand-drawn asymtotic curve. This means that there is no strict known formula for warp between 9 and 10 in The Next Generation. This does not mean all is lost. Wolfram Alpha can extrapolate values from the curve published in the Star Trek: The Next Generation Technical Manual.

Maximum Warp

The maximum speed of the NCC-1701D is

Extrapolating Warp 9.2 on Wolfram Alpha

We see that the maximum speed of the Enterprise-D is 1,649c.

Emergency Warp

Under emergency conditions, the Enterprise-D can travel at warp 9.6 for approximately 12 hours.

Extrapolating the speed for the Enterprise-D at warp 9.6.

This works out to be 1,909c.

USS Enterprise NCC-1701E

The maximum warp for the Enterprise-E is 9.995. Plugging this into Wolfram Alpha, we get

Extrapolating the Enterprise-E warp speed on Wolfram Alpha

We see that the Enterprise-E maximum warp is 14,597c.

Results

Ship Maximum Speed/c Emergency Speed/c
Orville 87,600.00
NX-01 127.26 140.61
NCC-1701 512
NCC-1701D 1,649 1,909
NCC-1701E 14,507

The Orville is by far the fastest ship compared to any of the Enterprises.


Also published on Medium.



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