I want my character's speed to ramp up using somewhat of a logarithmic formula. I am confused about how specifically I would implement this. I want the character to move fast with a little movement as as the movement gets larger the added contribution to speed is less and less. I said logarithmic function because this kind of mimics the shape of what I am after. Does anyone have an example of how this is done?


3 Answers 3


As much as I can tell you want something like this:

Target_Speed = some value;
Time = -log(Initial_Speed);

while(runnning) {
    Time += delta_time;
    Current_Speed = Target_Speed - exp(-Time);

    do some other stuff

And here is why this algorithm works:

We know logarithmic function exp(x) tend to approach 0 when x goes to negative infinity. So in order to make that logarithmic function become zero we should reduce Time to a very low value, or we can increase Time, and compute exp(-Time) instead. based on the current argument, it's easy to see when Time gets very large, -Time becomes real large negative and so exp(-Time) becomes almost zero.

And for the initial values: Target_Speed is your desired speed, and you can set it as you want. in the first cycle we want the Current_Speed to be zero, so Target_Speed - exp(-Time) should evaluate to zero.

        Target_Speed  = exp(-Time)
=>  log(Target_Speed) = log(exp(-Time)) = -Time
=> -log(Target_Speed) = Time

So simply by setting the initial value of Time to -log(Target_Speed) we will get what we wanted.

All that said I think my answer is exactly the same as Arne's except with little more information about how it's working!


You can add a curve and manually adjust the acceleration graph.

public AnimationCurve curve;

Then simply select it in the inspector and use a preset. To change speed, use:

currentSpeed = curve.Evaluate(t);

where "t" can be Time.time/5f or other value from 0 to 1.

If you want a more physical way then use rigidbody and rigidbody.AddRelativeForce(Vector3.forward);

  • \$\begingroup\$ what library is this code using? \$\endgroup\$
    – Ali1S232
    Jan 30, 2014 at 20:36
  • \$\begingroup\$ Sorry I'm new here, I thought it's a Unity question. My bad. \$\endgroup\$
    – Slasher
    Jan 30, 2014 at 21:33

each frame do this:

speed += 0.05;
pos += speed;
speed *= 0.99;

adjust parameters at will.

  • 2
    \$\begingroup\$ You should explain what this is doing and why it works in your answer. \$\endgroup\$ Jan 30, 2014 at 1:27
  • \$\begingroup\$ This much I know. But I want a way to specify a smooth formula for ramping down the effect of speed as it gets faster. \$\endgroup\$ Jan 30, 2014 at 1:41

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