Question jump to a specific height.

Hello everyone! I was interested in learning how to perform a jump to a specific height. To achieve this, I used the Jump method.

I derived the formula for calculating the jump height based on the specified number of units in the _jumpHeight variable. I used the ballistics formula to find the maximum height, which is h = V^2 / 2 * g. However, in order to make the character jump to the desired height in Unity, I had to subtract (Time.fixedDeltaTime * Physics.gravity.y) / 2. This works, but I'm not sure why.

Could someone please explain to me why this subtraction is necessary? I would appreciate a detailed explanation. I would also appreciate any other methods for performing a jump to a specified height. Thank you in advance!

Here's the code for my Jump method:

Code (CSharp):

1. public void Jump(InputAction.CallbackContext context)
2. {
3.     // I don't know why this crappy DeltaTime * gravity / 2 is used
4.     var velocity = Mathf.Sqrt(_jumpHeight * -2 * Physics.gravity.y) - (Time.fixedDeltaTime * Physics.gravity.y / 2);
5.     if (context.started && IsGrounded())
6.     {  
7.         _rb.AddForce(0f, velocity, 0f, ForceMode.VelocityChange);
8.     }
9. }

 

Do you have a drag set on the RigidBody, if any?

With a jump height of 1 m you have:
v = 4.43+0.10
0.10 makes the v only a little over 2% faster.

 

My RigidBody drag is set to zero. Angular drag doesn't affect on jump height.

It seems to me that Unity handles physics specific, so I need to adjust the formula. Perhaps @MelvMay could help me figure this out? Here's the code for 2D version:

Code (CSharp):

1. using Unity.Mathematics;
2. using UnityEngine;
3.  
4. public class Movement : MonoBehaviour
5. {
6.     [SerializeField, Range(0, 20)] float _jumpHeight = 5f;
7.     Rigidbody2D _rb;
8.     float _maxHeight = 0f;
9.  
10.     void Awake()
11.     {
12.         _rb = GetComponent<Rigidbody2D>();
13.         _maxHeight = _rb.position.y;
14.     }
15.  
16.     void FixedUpdate()
17.     {
18.         if (Input.GetKeyDown(KeyCode.Space))
19.         {
20.             Jump();
21.         }
22.  
23.         _maxHeight = Mathf.Max(_maxHeight, _rb.position.y);
24.         if (_rb.position.y < _maxHeight)
25.         {
26.             print(_maxHeight);
27.         }
28.     }
29.  
30.     void Jump()
31.     {
32.         var impulse = _rb.mass * (math.sqrt(-2 * Physics2D.gravity.y * _jumpHeight) - (Time.fixedDeltaTime * Physics.gravity.y / 2));
33.  
34.         if (IsGrounded())
35.         {
36.             _rb.AddForce(new Vector2(0f, impulse), ForceMode2D.Impulse);
37.         }
38.     }
39.  
40.     private bool IsGrounded()
41.     {
42.         return _rb.velocity.y == 0;
43.     }
44. }
45.  

Here are my RigidBody and Rigidbody2D settings: