45 Strafe

45° Strafe is a technique that grants more speed than regular movement.

It can be done by strafing and turning 45° degrees (hence the name).

45° Strafe can be performed by either:

• Turning 45° left and Strafing right.
• Turning 45° right and Strafing left.

The turning must be quick (< 1tick) and precise (at least ±11.5°, the closer to ±0° the better), so it's difficult to perform consistently.

Some jumps require the use of 45° strafe, such as 1bm 4.375b.

Effect on Movement

On every tick, the Player gains some acceleration depending on inputs and other factors.

• When moving forward (without strafing), the acceleration gained is scaled by $0.98$

• When strafing, the acceleration is scaled by $1.0$

Therefore, 45° Strafe is ${1.0 \over 0.98}$ times faster than regular movement (about 2% faster).

Special case: 45° Sneak

• When sneaking forward (without strafing), the acceleration gained is scaled by $0.98$
• When strafing while sneaking, the acceleration gained is scaled by $0.98{\sqrt {2}}$ (≈ 1.386)

45° Sneak is used for no momentum jumps (example).

Outside of parkour, it's notably used for bridging, as it's ~41% faster than regular sneaking.

Explanation

Below is a simplified version of the horizontal movement source code.

/* 
 * Code from Entity and EntityLivingBase
 * Unnecessary or unrelated code is stripped out
 */

public void onLivingUpdate()
{
    /* 
     * moveStrafing and moveForward represent relative movement.
     * moveStrafing = 1.0 if moving left, -1.0 if moving right, else 0.0
     * moveForward = 1.0 if moving forward, -1.0 if moving backward, else 0.0
     *
     * Furthermore, moveStrafing and moveForward *= 0.3 if the player is sneaking.
     */

    this.moveStrafing *= 0.98F;
    this.moveForward *= 0.98F;
    this.moveEntityWithHeading(this.moveStrafing, this.moveForward);
}



public void moveEntityWithHeading(float strafe, float forward)
{
    /* inertia determines how much speed is conserved onto the next tick */
    float mult = 0.91F;
    if (this.onGround)
    {
        /* Get slipperiness 1 block below the player */
        mult *= getBlockSlipperinessAt(this.posX, this.getEntityBoundingBox().minY - 1, this.posZ);
    }

    /* acceleration = (0.6*0.91)^3 / (slipperiness*0.91)^3) */
    float acceleration = 0.16277136F / (mult * mult * mult);

    float movementFactor;
    if (this.onGround)
        movementFactor = this.landMovementFactor * acceleration;
        /* base: 0.1; x1.3 if sprinting, affected by potion effects. */

    else
        movementFactor = this.airMovementFactor; 
        /* base: 0.02; x1.3 if sprinting */

    this.updateMotionXZ(strafe, forward, movementFactor); 
    this.moveEntity(this.motionX, this.motionY, this.motionZ);

    this.motionY -= 0.08D; /* gravity */
    this.motionY *= 0.98D; /* drag */

    this.motionX *= mult;
    this.motionZ *= mult;
}



public void updateMotionXZ(float strafe, float forward, float movementFactor)
{
    /*
     * This function is responsible for the existence of 45° strafe. The geometry doesn't seem to make sense...
     * Note that:
     *     - Sprint multiplier is contained within "movementFactor"
     *     - Sneak multiplier is contained within "strafe" and "forward"
     * This is likely because Sneaking was implemented long before Sprinting
     */
    float distance = strafe * strafe + forward * forward;

    if (distance >= 1.0E-4F)
    {
        distance = MathHelper.sqrt_float(distance);
            
        if (distance < 1.0F)
            distance = 1.0F;

        distance = movementFactor / distance;
        strafe = strafe * distance;
        forward = forward * distance;
        float sinYaw = MathHelper.sin(this.rotationYaw * Math.PI / 180.0F);
        float cosYaw = MathHelper.cos(this.rotationYaw * Math.PI / 180.0F);
        this.motionX += strafe * cosYaw - forward * sinYaw;
        this.motionZ += forward * cosYaw + strafe * sinYaw;
    }
}