diff --git a/common/systems/tests/phys/basic.rs b/common/systems/tests/phys/basic.rs
index 38b9e2fe42..dfa7855d71 100644
--- a/common/systems/tests/phys/basic.rs
+++ b/common/systems/tests/phys/basic.rs
@@ -328,21 +328,25 @@ fn physics_theory() -> Result<(), Box<dyn Error>> {
         let air_density = 1.225_f64;
         let c = air_friction_co * air_friction_area * 0.5 * air_density * mass ;
 
-        let acc = 9.2_f64 * move_dir; // btw: cant accelerate faster than gravity on foot
+        const MAX_ACC: f64 = 9.2;
+        let acc = MAX_ACC * move_dir; // btw: cant accelerate faster than gravity on foot
         let old_vel = vel;
 
         // controller
         // I know what you think, wtf, yep: https://math.stackexchange.com/questions/1929436/line-integral-of-force-of-air-resistanc
         // basically an integral of the air resistance formula which scales with v^2 transformed with an ODE.
 
-        // The function besically takes its last result calculates the inverse* of it, adds the newly get speed to it and then run tanh again
-        // *inverse of the tanh and the factors before.
-        let past_fak = (c / (mass * acc.abs() ) ).sqrt() * old_vel;
-        // the original algorithm isn't able to keep a speed over the terminal velocity based on acc. however that is necessary, e.g. for pushbacks, falling, external factors and stopping (because of we stop acc would be 0 and the  terminal vel would be 0 too)
-        // here we decide to reduce that factor by c each second.
-        let over_vel_keep = (past_fak * c.powf(dt)).max(1.0) * past_fak.signum(); //TODO signum needed
-        let vel = ( ((mass * acc.abs() ) / c ).sqrt() * over_vel_keep) * ( ( past_fak.clamp(-1.0, 1.0) ).atanh() + acc.signum() * (c * acc.abs() / mass).sqrt() * dt ).tanh();
-        //let vel =  ((mass * acc.abs() + old_acc ) / c).sqrt() * ( ( ( (c / (mass * acc.abs() ) ).sqrt() * old_vel).clamp(-1.0, 1.0) ).atanh() + acc.signum() * (c * acc.abs() / mass).sqrt() * dt ).tanh();
+        // terminal velocity equals the maximum velocity that can be reached by acc alone
+        let vel_t = (mass * acc.abs() / c ).sqrt();
+        let _vel_tm = (mass * MAX_ACC / c ).sqrt();
+
+        // if our old_vel is bigger than vel_t we can use `coth(x) = 1/tanh(x)` and `acoth(x) = atanh(1/x)`
+        let revert_fak = old_vel / vel_t ;
+        let vel = if revert_fak.abs() >= 1.0 {
+            vel_t / ( ( 1.0 / revert_fak).atanh() + acc.signum() * (c * acc.abs()).sqrt() * dt ).tanh()
+        } else {
+            vel_t * ( ( revert_fak ).atanh() + acc.signum() * (c * acc.abs()).sqrt() * dt ).tanh()
+        };
 
         //physics
         let distance_last = mass / c * ( ( ( old_vel * (c/acc / mass).sqrt()).atanh() ).cosh() ).ln();
@@ -358,7 +362,7 @@ fn physics_theory() -> Result<(), Box<dyn Error>> {
 
 
         let ending = ((i+1) as f64 *dt * 10.0).round() as i64;
-        let line = format!("[{:0>2.1}]:    move_dir: {:0>1.1},    over_vel_keep: {:0>4.4},    acc: {:0>4.4},    vel: {:0>4.4},    dist: {:0>7.4},    dist: {:0>7.4},    pos: {:0>7.4},    c: {:0>4.4}", (i+1) as f64 *dt, move_dir, over_vel_keep, acc, vel, distance_last, distance, pos, c);
+        let line = format!("[{:0>2.1}]:    move_dir: {:0>1.1},    acc: {:0>4.4},    revert_fak: {:0>4.4},    vel: {:0>4.4},    dist: {:0>7.4},    dist: {:0>7.4},    pos: {:0>7.4},    c: {:0>4.4}", (i+1) as f64 *dt, move_dir, acc, revert_fak, vel, distance_last, distance, pos, c);
         if ending % 10 == 0 {
             println!("\x1b[91m{}\x1b[0m", line)
         } else if ending % 2 != 0 {