26.2 Kinetic Physics and Drag

Kinetic Physics & Dynamic Drag Floor Scaling — MC 26.2

This page details the aerodynamic physics model, dynamic drag floor scaling equations, and bytecode integration powering Elytra fall-flying mechanics in Max Elytra Fly Speed (MC 26.2).

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📋 Subsystem Infobox

Parameter	Technical Details
Subsystem Name	Aerodynamic Drag Floor Scaling & Velocity Limiting
Java Implementation	net.instantgratification.maxelytraflyspeed.util.ElytraDragHelper
Bytecode Mixin	net.instantgratification.maxelytraflyspeed.mixin.LivingEntityMixin
Target Methods	LivingEntity.updateFallFlyingMovement, LivingEntity.travelFallFlying
Controlling GameRule	max-elytra-fly-speed:max_elytra_fly_speed (Default: 50)
Algorithmic Complexity	$\mathcal{O}(1)$ time complexity, zero memory allocations per tick
Parity Standard	Exact Vanilla $0.99H / 0.98V$ drag at $\le 50\text{ Blocks/Sec}$

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🎮 Step-by-Step Player Workflow

In vanilla Minecraft, players attempting high-speed Elytra flight experience an artificial "velocity wall": vanilla hardcoded drag factors ($0.99\times$ horizontal and $0.98\times$ vertical) bleed off speed rapidly, making high-speed dives short-lived.

With Max Elytra Fly Speed:

1. Takeoff & Fall-Flying: The player deploys Elytra wings by pressing Jump mid-air.
2. Diving for Acceleration: Pitching the camera downward converts gravitational potential energy into kinetic velocity.
3. Dynamic Drag Relaxation: As server administrators increase max_elytra_fly_speed above $50\text{ BPS}$, the aerodynamic drag loss smoothly decreases in inverse proportion.
4. Sustained High-Speed Glide: Pulling up into a horizontal glide preserves momentum across thousands of blocks without sudden velocity drops.
5. Hard Velocity Clamping: If external explosions, external mods, or extreme dives accelerate the player beyond the configured ceiling, the velocity vector is smoothly scaled down without altering flight direction.

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📐 Mathematical Aerodynamic Models

1. Speed Ratio Scaling

The dynamic scaling factor $\text{speedRatio}$ compares the configured maximum speed ceiling against the vanilla baseline ($50.0\text{ BPS}$):

$$\text{speedRatio} = \max\left(1.0, \frac{\text{maxSpeedBps}}{50.0}\right)$$

• When $\text{maxSpeedBps} \le 50$: $\text{speedRatio} = 1.0$ (100% vanilla physics parity).
• When $\text{maxSpeedBps} > 50$: $\text{speedRatio}$ scales linearly with the configured limit (e.g. $2.0$ at $100\text{ BPS}$, $4.0$ at $200\text{ BPS}$).

2. Inverse Drag Floor Equations

Drag loss per tick is computed by relaxing the baseline vanilla drag loss ($0.01$ horizontal, $0.02$ vertical) by $\text{speedRatio}$:

$$\text{dragLossH} = \frac{0.01}{\text{speedRatio}}, \quad \text{dragLossV} = \frac{0.02}{\text{speedRatio}}$$

3. Velocity Damping Transformation

Every game tick ($20\text{ ticks} = 1\text{ second}$), the movement vector $\vec{v} = \langle v_x, v_y, v_z \rangle$ is updated via the Hadamard product:

$$\vec{v}_{t+1} = \vec{v}_t \odot \begin{pmatrix} 1.0 - \text{dragLossH} \ 1.0 - \text{dragLossV} \ 1.0 - \text{dragLossH} \end{pmatrix}$$

4. Hard Velocity Ceiling Clamping

If the magnitude $|\vec{v}|$ exceeds the maximum tick speed $v_{\text{max_ticks}} = \frac{\text{maxSpeedBps}}{20.0}$:

$$\vec{v}_{\text{clamped}} = \vec{v} \times \left(\frac{v_{\text{max_ticks}}}{|\vec{v}|}\right)$$

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📊 Visual ASCII Damping Diagram

 Drag Loss (%)
  2.0% |   * (Vertical Vanilla Baseline: 0.98x)
       |    \
  1.0% |     * (Horizontal Vanilla Baseline: 0.99x)
       |      \
  0.5% |       *---* (100 BPS: 0.995x / 0.990x)
       |            \
 0.25% |             *---*---* (200 BPS: 0.9975x / 0.9950x)
       +----------------------------------------------------> Configured Max Speed (BPS)
       0    30   50   100  200  300  400  500

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📑 Drag Multiplier Reference Table

Max Speed Setting	$\text{speedRatio}$	Horizontal Drag Loss ($\text{dragLossH}$)	Vertical Drag Loss ($\text{dragLossV}$)	Horizontal Multiplier	Vertical Multiplier	Velocity Ceiling (Blocks/Tick)
30 BPS	$1.00$	$0.0100$ ($1.00%$)	$0.0200$ ($2.00%$)	$0.9900\times$	$0.9800\times$	$1.50\text{ blocks/tick}$
50 BPS (Default)	$1.00$	$0.0100$ ($1.00%$)	$0.0200$ ($2.00%$)	$0.9900\times$	$0.9800\times$	$2.50\text{ blocks/tick}$
100 BPS	$2.00$	$0.0050$ ($0.50%$)	$0.0100$ ($1.00%$)	$0.9950\times$	$0.9900\times$	$5.00\text{ blocks/tick}$
200 BPS	$4.00$	$0.0025$ ($0.25%$)	$0.0050$ ($0.50%$)	$0.9975\times$	$0.9950\times$	$10.00\text{ blocks/tick}$
500 BPS	$10.00$	$0.0010$ ($0.10%$)	$0.0020$ ($0.20%$)	$0.9990\times$	$0.9980\times$	$25.00\text{ blocks/tick}$

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💻 Developer & Bytecode Mixin Hooks

1. ElytraDragHelper.java

package net.instantgratification.maxelytraflyspeed.util;

import net.minecraft.world.phys.Vec3;

public final class ElytraDragHelper {
    public static Vec3 calculateFallFlyingDrag(Vec3 movement, int maxSpeedBps) {
        if (movement == null) return Vec3.ZERO;

        double speedRatio = Math.max(1.0, maxSpeedBps / 50.0);
        double dragLossH = 0.01 / speedRatio;
        double dragLossV = 0.02 / speedRatio;

        return movement.multiply(1.0 - dragLossH, 1.0 - dragLossV, 1.0 - dragLossH);
    }
}

2. Bytecode Redirection in LivingEntityMixin.java

• Mixin Target: LivingEntity.class
• Injection 1 (@Redirect): Redirects Vec3.multiply(DDD) in updateFallFlyingMovement to apply dynamic drag multipliers instead of hardcoded constants.
• Injection 2 (@Inject): Intercepts LivingEntity.travelFallFlying right before LivingEntity.move() to enforce hard speed clamping at maxSpeedTicks.

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