Accelerating smoothly to a given level

Questions & Answers
1

Hi there.
I’m tinkering with a basic 3D submarine game and want to make my sub level out smoothly at a given depth.

In manual control, the bow angle is controlled by the vertical axis. Its value is applied to a rotational acceleration which is added to a rotational speed around the X-axis (making it point up/down smoothly). The angle is subsequently clamped to +/- 80 degrees. The vessels position is then calculated by angle * speed thus increasing/decreasing depth.

However, I wish to set a depth and have the sub automatically ‘slerp’ to that depth using its usual rotational acceleration/speed values to calculate the slopes and curves.

I’m not sure how to calculate when the vessel should begin to level out in time to get to the correct depth.

Can anyone suggest the correct way to go about this or point me towards the correct formulas?

2

I’m not using physics, want to avoid doing that if at all possible. Even if I was i’d still require the angle of attack to decrease before the assigned value. Also, the sub passed the assigned value and it still had vertical velocity then it would pitch the opposite direction to try to get to it creating a bobbing motion.

I need the angle of attack of the sub to decrease before it gets to the assigned depth and level out smoothly rather. I’m sure this problem must be similar to making a car steer to a certain heading smoothly or making a car stop on a given spot employing smooth movements. My usually good googling is failing me.