Two-Tier Firework Rocket Propulsion & Vector Convergence — MC 26.2

This page details the mathematical propulsion algorithms, state transitions, and vector difference convergence powering firework rocket boosting in Max Elytra Fly Speed (MC 26.2).

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📋 Subsystem Infobox

Parameter	Technical Details
Subsystem Name	Two-Tier Firework Rocket Propulsion & Vector Convergence
Java Implementation	net.instantgratification.maxelytraflyspeed.util.RocketBoostHelper
Bytecode Mixin	net.instantgratification.maxelytraflyspeed.mixin.FireworkRocketEntityMixin
Target Method	FireworkRocketEntity.tick
Controlling GameRules	elytra_initial_boost_speed (Default: 30), elytra_high_speed_acceleration (Default: 15)
Algorithmic Complexity	$\mathcal{O}(1)$ time complexity, zero memory allocations per tick
Convergence Rate	$15%\text{ vector difference per tick}$ ($f_{\text{acc}} = 0.15$)

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🎮 Step-by-Step Player Workflow

In vanilla Minecraft, firework rockets apply a fixed formula designed solely for low-speed flight: $$\vec{b}{\text{vanilla}} = \vec{u}{\text{look}} \times 0.1 + \left(\vec{u}_{\text{look}} \times 1.5 - \vec{v}\right) \times 0.5$$ When flying above $30\text{ BPS}$ ($1.5\text{ blocks/tick}$), the vanilla formula actively decelerates the player!

Max Elytra Fly Speed introduces a Two-Tier Propulsion Engine:

1. Tier 1 — Snappy Launch Boost ($v < 30\text{ BPS}$): When launching from a standstill or slow glide, the rocket delivers instant, snappy vanilla acceleration ($50%$ convergence per tick) to quickly reach cruising velocity.
2. Tier 2 — High-Speed Vector Convergence ($v \ge 30\text{ BPS}$): Above $30\text{ BPS}$, the rocket transitions to proportional vector difference convergence, pulling the flight vector smoothly towards the camera look angle scaled by the configured maximum speed ceiling.
3. Continuous Re-Orientation: As the player turns their camera, the high-speed convergence factor continuously aligns their momentum with the new look direction without jarring angular snapping.

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📐 Mathematical Propulsion Models

1. Tier 1: Snappy Initial Acceleration

When the current velocity magnitude $v_{\text{current}} = |\vec{v}{\text{old}}|$ is below the initial boost threshold ($v{\text{initial_ticks}} = \frac{\text{initialBoostSpeedBps}}{20.0}$):

$$\vec{b}{\text{initial}} = \vec{u}{\text{look}} \times 0.1 + \left(\vec{u}{\text{look}} \times v{\text{initial_ticks}} - \vec{v}_{\text{old}}\right) \times 0.5$$

2. Tier 2: Proportional High-Speed Vector Convergence

When $v_{\text{current}} \ge v_{\text{initial_ticks}}$, the boost vector calculates the difference between the target velocity $\vec{v}{\text{target}} = \vec{u}{\text{look}} \times v_{\text{max_ticks}}$ and the current velocity:

$$\vec{b}{\text{high}} = \vec{u}{\text{look}} \times 0.1 + \left(\vec{u}{\text{look}} \times v{\text{max_ticks}} - \vec{v}{\text{old}}\right) \times f{\text{acc}}$$

where $f_{\text{acc}}$ is the high-speed acceleration factor: $$f_{\text{acc}} = \max\left(0.05, \frac{\text{highAccPermille}}{100.0}\right)$$ (Default: $15 \implies f_{\text{acc}} = 0.15$ or $15%\text{ convergence per tick}$).

3. Vector Sum & Velocity Clamping

The final target movement is combined and clamped to ensure it never exceeds the configured ceiling:

$$\vec{v}{\text{target_movement}} = \vec{v}{\text{old}} + \vec{b}$$

$$\vec{v}{\text{final}} = \begin{cases} \vec{v}{\text{target_movement}} \times \left(\frac{v_{\text{max_ticks}}}{|\vec{v}{\text{target_movement}}|}\right) & \text{if } |\vec{v}{\text{target_movement}}| > v_{\text{max_ticks}} \ \vec{v}_{\text{target_movement}} & \text{otherwise} \end{cases}$$

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📊 Visual State Machine Flowchart

                 [ PLAYER USES FIREWORK ROCKET ]
                                |
                                v
               Is Current Velocity < 30 BPS?
                             /     \
                     (YES)  /       \  (NO)
                           v         v
             [ TIER 1: SNAPPY BOOST ]  [ TIER 2: HIGH-SPEED CONVERGENCE ]
             • 50% convergence         • 15% proportional convergence
             • Quick launch to 30 BPS  • Smooth pull toward look vector * maxSpeed
                           \         /
                            v       v
                 [ VECTOR SUM & SPEED CLAMP ]
                 • Add boost to deltaMovement
                 • Clamp magnitude <= maxSpeedBps / 20.0

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📑 Acceleration Time Reference Table

Assuming starting speed of $30\text{ BPS}$ ($1.5\text{ blocks/tick}$) and look angle aligned with flight path:

Max Speed Setting	Acceleration Setting ($f_{\text{acc}}$)	Ticks to Reach 90% Max Speed	Seconds to Reach 90% Max Speed	Blocks Traveled During Boost
50 BPS	$15%\text{ / tick}$ (Default)	$\approx 14\text{ ticks}$	$0.70\text{ seconds}$	$\approx 29\text{ blocks}$
100 BPS	$15%\text{ / tick}$ (Default)	$\approx 15\text{ ticks}$	$0.75\text{ seconds}$	$\approx 52\text{ blocks}$
100 BPS	$25%\text{ / tick}$ (Fast)	$\approx 9\text{ ticks}$	$0.45\text{ seconds}$	$\approx 35\text{ blocks}$
200 BPS	$15%\text{ / tick}$ (Default)	$\approx 16\text{ ticks}$	$0.80\text{ seconds}$	$\approx 98\text{ blocks}$
200 BPS	$50%\text{ / tick}$ (Supersonic)	$\approx 5\text{ ticks}$	$0.25\text{ seconds}$	$\approx 38\text{ blocks}$
500 BPS	$15%\text{ / tick}$ (Default)	$\approx 17\text{ ticks}$	$0.85\text{ seconds}$	$\approx 235\text{ blocks}$

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💻 Developer & Bytecode Mixin Hooks

1. RocketBoostHelper.java

package net.instantgratification.maxelytraflyspeed.util;

import net.minecraft.world.phys.Vec3;

public final class RocketBoostHelper {
    public static Vec3 calculateBoostMovement(
        Vec3 oldMovement,
        Vec3 lookAngle,
        double initialBoostSpeedTicks,
        double maxSpeedTicks,
        double highAccFactor
    ) {
        if (oldMovement == null) oldMovement = Vec3.ZERO;
        if (lookAngle == null) lookAngle = Vec3.ZERO;

        double currentSpeed = oldMovement.length();
        Vec3 targetBoost;

        if (currentSpeed < initialBoostSpeedTicks) {
            targetBoost = lookAngle.scale(0.1).add(
                lookAngle.scale(initialBoostSpeedTicks).subtract(oldMovement).scale(0.5)
            );
        } else {
            Vec3 targetVelocity = lookAngle.scale(maxSpeedTicks);
            targetBoost = lookAngle.scale(0.1).add(
                targetVelocity.subtract(oldMovement).scale(highAccFactor)
            );
        }

        Vec3 targetMovement = oldMovement.add(targetBoost);
        double targetSpeed = targetMovement.length();
        if (targetSpeed > maxSpeedTicks && targetSpeed > 0.0) {
            targetMovement = targetMovement.scale(maxSpeedTicks / targetSpeed);
        }
        return targetMovement;
    }
}

2. Bytecode Injection in FireworkRocketEntityMixin.java

• Mixin Target: FireworkRocketEntity.class
• Injection (@Redirect): Redirects entity.setDeltaMovement() inside tick() to apply RocketBoostHelper.calculateBoostMovement().

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