Resolved How to make deterministic jump? Different jump height by different target frame rate.

There is a simple formula to calculate initial velocity from given jump height:

Code (CSharp):

1. initialVelocity = Mathf.Sqrt(-2.0f * gravity * jumpHeight);

But the reached jump height is different across different target frame rates.
By Application.targetFrameRate = -1 ball reaches the jumpHeight almost perfectly. By targetFrameRate = 30 there is a small gap. I don't get it why it happens, i thought that using deltaTime should be enough.

Project files attached.

here is the code

Code (CSharp):

1.  
2. public float jumpHeight;
3.  
4.     float gravity = -9.81f;
5.     private float initialVelocity;
6.     private float velocity;
7.  
8.     private void jump()
9.     {
10.         initialVelocity = Mathf.Sqrt(-2.0f * gravity * jumpHeight);
11.         velocity = initialVelocity;
12.     }
13.  
14.     private void Update()
15.     {
16.         if (Input.GetMouseButtonDown(0))
17.         {
18.             transform.position = Vector3.zero;
19.             jump();
20.         }
21.  
22.         if (velocity > 0)
23.         {
24.             // Apply gravity to the velocity
25.             velocity += gravity * Time.deltaTime;
26.  
27.             // Move the ball based on the current velocity
28.             transform.Translate(Vector3.up * velocity * Time.deltaTime);
29.         }
30.  
31.     }

 

It's a discrete simulation of a continuous phenomena. Putting it in Update() almost guarantees varying timesteps.

Perhaps your needs would be better suited via FixedUpdate() ? You haven't said your needs.

Two good discussions on Update() vs FixedUpdate() timing:

https://jacksondunstan.com/articles/4824

https://johnaustin.io/articles/2019/fix-your-unity-timestep

Here is some timing diagram help:

https://docs.unity3d.com/Manual/ExecutionOrder.html

Here is an abbreviated and better-annotated version of the above:

https://forum.unity.com/threads/a-c...ution-order-of-unity-event-functions.1381647/

 

While it won't be 100% deterministic due to floating point precision limitations, you can greatly reduce effect of framerate on you jump if you use the correct formula for calculating how much to move the player every frame.

Code (CSharp):

1. public float jumpHeight;
2.     float gravity = -9.81f;
3.     private float initialVelocity;
4.     private float velocity;
5.     private void jump()
6.     {
7.         initialVelocity = Mathf.Sqrt(-2.0f * gravity * jumpHeight);
8.         velocity = initialVelocity;
9.     }
10.     private void Update()
11.     {
12.         if (Input.GetMouseButtonDown(0))
13.         {
14.             transform.position = Vector3.zero;
15.             jump();
16.         }
17.         if (velocity > 0)
18.         {
19.             // Δx= v0*t + (1/2)*a*t²
20.             float displacement = velocity * Time.deltaTime + 0.5f * gravity * (Time.deltaTime * Time.deltaTime);
21.  
22.             // Apply gravity to the velocity
23.             velocity += gravity * Time.deltaTime;
24.             // Move the ball based on the current velocity
25.             transform.Translate(Vector3.up * displacement);
26.         }
27.     }

If you apply gravity to the velocity first, you are displacing the object as if it moved the entire frame time at that final velocity, which is not true: if you were to increase the framerate by 1000x, the velocity at each of these sub-frames would be different because it changes due to the acceleration at each step.

That formula calculates the sum of the displacement of "infinitely small" sub-steps between the previous velocity and the new one. Since gravity is constant, velocity increases linearly and the sum of the displacement of infinite sub-steps can be calculated precisely by taking the average of the old and new velocity values (aka: the integral).

For reference:
https://www.khanacademy.org/science...ic-formulas/a/what-are-the-kinematic-formulas

 

Wow, you solved the problem perfectly, now the given jump height is reached at any frame rate. I'm lacking some kinematic formulas, have to dive into, thank you Sir