Beginner question about using deltaTime

So I’ve got Game manager code

public static string GamePhase = "Planning";
public static float MovementTimer = 2.0f;
private static float MovementCountdown = MovementTimer;

// Use this for initialization
void Start () {

}

// Update is called once per frame
void Update () {

	if(Input.GetButtonDown("Submit") && GamePhase == "Planning")
	{
		MovementCountdown = MovementTimer;
		GamePhase = "Movement";
		Debug.Log ("Phase is now" + GamePhase);
	}

	if(GamePhase == "Movement")
	{
		MovementCountdown -= Time.deltaTime;
		if (MovementCountdown <= 0.0f) 
		{
			GamePhase = "Planning";
			Debug.Log ("Phase is now" + GamePhase);
		}
	
	}
		
}

and unit code

public float Heading = 90.0f;
public float Speed = 1.0f;
void Start () {
	
}

// Update is called once per frame
void LateUpdate () {
	if (GamePhaseManager.GamePhase == "Movement") 
	{
		var x = Time.deltaTime * Heading / GamePhaseManager.MovementTimer;
		var z = Time.deltaTime * Speed / GamePhaseManager.MovementTimer;
		transform.Rotate(0, x, 0);
		transform.Translate(0, 0, z);
		Debug.Log ("Ship is moving!");
			
	}
}

}

In theory this should make my ship travel a distance of 1 length while turning 90 degrees over a time period of 2 seconds each time I hit the submit button. However, every time it executes, the angle ends up off by ~.5 degrees, and if I try to do a full circle (4 executions) I end up at position x = 0.1019182, position z =-0.1206948, and rotation y = -1.814. What do I need to change so that the movement ends up more precise (exactly 90 degrees every turn)?

It’s because your gameobject is not rotating on the last frame of the rotation cycle because you are rotating in LateUpdate and your Update method from GamePhaseManager sets the phase to planning before your LateUpdate gets a chance to rotate the last increment.

Consider your game is running at 60 FPS then the approx deltaTime is 0.0166 (1/60). So your each rotation value of x as per your line of code:

var x = Time.deltaTime * Heading / GamePhaseManager.MovementTimer;

will be:

x = 0.0166 * (90/2) = 0.747 (~0.5)

But since deltaTime is not exactly the same as we have assumed (0.0166) you are getting an approx rotation delta lag of 0.5.

You can change your LateUpdate to Update and since you want to have your unit code run after GamePhaseManager you can set the script execution order for these two scripts. Or rather than doing that you can apply correction at the end when rotation ends to have your object rotate to exact value.