Question

I would like to be able to roughly determine the maximum horizontal flight speed of any superpowered individual using only the maximum acceleration that person can produce. To do this, I will need a formula for which I can simply enter the maximum acceleration in g's, or maxiumum force in Newtons, and then get a velocity out.

How flight works:
The kind of flight relevant to this questions works by accelerating the individual's body in a given direction, as if their body were being pulled in a specific direction by a gravitational field of a certain strength. A flying person's top speed is determined only by the maximum acceleration they can achieve, and their interactions with the atmosphere. If they were to fly in space, they could continue to accelerate indefinitely. In other words, there is no hard limit to the speed of flight, except for that imposed by air resistance.

For Example
Someone who can output a maximum of 2g of acceleration could fly at a top speed of roughly 240 km/h. This is because the terminal velocity of a person is roughly 240 km/h, and this flying individual could output 1g of acceleration upwards in order to counteract gravity and hover, and then another 1g sideways in order to fly in that direction. However, I doubt I can simply multiply this speed by a person's sideways acceleration to get a new top speed. E.g: I doubt someone producing 2g of sideways acceleration would travel at 480 km/h, and 3g at 760 km/h, etc.

Assumptions:
The person is a sphere with a radius of 0.5m, and weighs 100kg.
The person is flying at sea level.
1g of acceleration is used to maintain altitude with the rest being used for forward movement
The person will continue accelerating until drag equals the force they produce with their acceleration.
The person is strong and durable enough to be unaffected by any adverse affects from flying at great speed.
What I Am Looking For in an Answer
A good answer will provide a formula which will output a speed dependant upon the force or acceleration, and hopefully an explanation of all the relevant variables of the formula.

I am not sure if this is necessary, but perhaps it would be useful to split the answer into 2 separate formulae, one for subsonic speeds and one for supersonic speeds.

While I am looking for hard answers using equations and known science, I am not using the hard-science tag, as I know how people get when you use that with questions relating to magic or superpowers.

Why I am Asking
Since this kind of flight has a relatively rigid definition of how it functions, it would be useful to be able to roughly determine any superheroes' max flight speed based on how much weight they could hold and hover with. For example, if one supe is capable of hovering while lifting a car above their head, they must be capable of producing at least 16gs of acceleration (and ~16,000 Newtons) upwards (100kg bodyweight, 1500kg car), and necessarily must be able to fly faster than someone only capable of hovering while holding another person. Being able to estimate their flight speeds is then useful for powerscaling and planning conflicts.

Answer 1

The formula to calculate the maximum horizontal flight speed of a superpowered individual is v = sqrt((2 * a * r) / p), where v is the velocity, a is the acceleration, r is the radius of the person, and p is the fluid density.

Step-by-step explanation:

To determine the maximum horizontal flight speed of a superpowered individual, we need to consider the concept of terminal velocity.

Terminal velocity is the maximum speed an object can reach when the drag force equals the force exerted by the acceleration. In this case, the acceleration is the maximum acceleration the person can produce.

The formula to calculate terminal velocity is: v = sqrt((2 * a * r) / p), where v is the velocity, a is the acceleration in m/s², r is the radius of the person in meters, and p is the fluid density (air in this case).

Using this formula, we can estimate the maximum horizontal flight speed of a superpowered individual based on their maximum acceleration.

The result will depend on the parameters of the person, such as their mass and size.