- #1
Matej
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How could I express the speed of an object as a function of time if the object is accelerating with a constant power output and is being affected by quadratic (Rayleigh) drag?
How Do You Model Speed with Constant Power and Quadratic Drag?
In summary, to express the speed of a submarine as a function of time when it is accelerating with a constant power output and affected by quadratic drag, one must consider the free-body diagram and relevant forces, including thrust and drag. The thrust is usually determined empirically or numerically, and for low velocities, there is static thrust data. To find the speed as a function of time, the acceleration from the net force must be integrated numerically.
- #2
SteamKing
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What type of object?
- #3
Matej
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Well, it's supposed to be a submarine.
As far as the physics go, it's a solid object with density equal to the density of the liquid
Anything else?
As far as the physics go, it's a solid object with density equal to the density of the liquid
Anything else?
- #4
SteamKing
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As a start, I would draw a free-body diagram and add the relevant forces. Since it is a submarine, the power produced by the propulsion machinery is converted into thrust, either by turning a propeller or by means more exotic. The drag is proportional to the velocity squared and acts to oppose the thrust. Since the sub is accelerating, then T - D is positive, and T - D = m a, where m is the mass of the submarine, and a = dv/dt.
- #5
A.T.
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And in general the thurst will not be constant for constant power input, but depend on the speed.SteamKing said:
- #6
Matej
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A.T. said:
And that's the point where I got stuck. I found an equation that works if the thrust is constant but that is not the case here.
Perhaps if I expressed drag as a loss in energy (speed3) it might be simpler.
Not quite sure though, we haven't done anything like this at school so far and it might be a few years till we do.
- #7
A.T.
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You won't get an analytic solution for this. The thrust itself is not some simple function but usually derived empirically or numerically. You have a chart like this:Matej said:
And get the thrust by:
thrust = (efficiency * shaft_power) / velocity
To get the speed as function of time you have to integrate the acceleration from the net force (thrust - drag) numerically. For low velocities there is static thrust data.
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1. How is speed calculated as a function of time?
Speed as a function of time is calculated by dividing the distance traveled by the time it took to travel that distance. This is represented by the equation: speed = distance/time.
2. Is speed always constant as a function of time?
No, speed can vary as a function of time. This is known as acceleration, which is the change in speed over time. If the speed is increasing, it is called positive acceleration, and if the speed is decreasing, it is called negative acceleration or deceleration.
3. How is the speed-time graph related to speed as a function of time?
The speed-time graph is a visual representation of speed as a function of time. The slope of the graph at any given point represents the speed at that particular time. A steeper slope indicates a higher speed, while a flatter slope indicates a lower speed.
4. What is the difference between average speed and instantaneous speed as a function of time?
Average speed is the total distance traveled divided by the total time taken, while instantaneous speed is the speed at a specific moment in time. Average speed gives an overall understanding of how fast an object is moving, while instantaneous speed gives the speed at a particular point in time.
5. How does mass affect speed as a function of time?
Mass does not directly affect speed as a function of time. However, it does affect the acceleration of an object. According to Newton's Second Law of Motion, the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This means that a larger mass will require more force to accelerate, resulting in a slower speed as a function of time.
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