How to calculate projectile trajectory and power for accurate targeting in Scratch
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PE
PhysicsEngine_Dev
Posted on January 25, 2024 • Advanced
🎯 Projectile trajectory calculation challenge
Hey physics enthusiasts! I’m building a 2D platformer where enemies need to shoot arrows at the player with realistic physics. The challenge is calculating the exact power and angle needed to hit a moving target! 🏹
My current setup:
- Arrows have xv (horizontal velocity) and yv (vertical velocity) variables
- Gravity affects the yv over time
- Player can be at any position and moving
- Enemies need to predict where to aim
- Need realistic ballistic trajectory
I’ve tried basic angle calculations but they don’t account for gravity drop-off. The arrows either overshoot or fall short. I need a proper physics-based solution that can:
- Calculate the required initial velocity components
- Account for gravity in trajectory prediction
- Handle different distances and heights
- Predict player movement for leading shots
- Work efficiently in real-time
Any math wizards who can help with the ballistics calculations? 🤓
BM
BallisticsMath_Expert
Replied 3 hours later • ⭐ Best Answer
Excellent physics challenge @PhysicsEngine_Dev! Projectile motion with gravity is a classic ballistics problem. Here’s a complete solution:
🎯 Projectile Physics System Flow
Here’s how accurate trajectory calculation works:
flowchart TD
A[🎯 Target Detected] --> B[Get Positions]
B --> C[Calculate Distance]
B --> D[Calculate Height Difference]
C --> E[Apply Trajectory Formula]
D --> E
E --> F[Calculate Initial Velocity]
F --> G[Split into X/Y Components]
G --> H[Launch Projectile]
H --> I[Apply Gravity Each Frame]
I --> J{Hit Target?}
J -->|Yes| K[Success!]
J -->|No| L[Continue Trajectory]
L --> I
K --> M[Impact Effect]
style A fill:#e1f5fe
style E fill:#e8f5e8
style F fill:#fff3e0
style K fill:#e8f5e8
style M fill:#fce4ec
🧮 Core Trajectory Mathematics
The fundamental physics equations for projectile motion:
// Core trajectory calculation system define calculate trajectory (target x) (target y) (launch x) (launch y) (gravity) // Calculate distance and height difference set [distance x v] to ((target x) - (launch x)) set [distance y v] to ((target y) - (launch y)) set [total distance v] to ([sqrt v] of (((distance x) * (distance x)) + ((distance y) * (distance y)))) // Calculate optimal launch angle (45 degrees for max range) set [launch angle v] to [45] // Calculate required initial velocity set [velocity needed v] to ([sqrt v] of (((total distance) * (gravity)) / ([sin v] of ((launch angle) * [2])))) // Split into X and Y components set [initial x velocity v] to ((velocity needed) * ([cos v] of (launch angle))) set [initial y velocity v] to ((velocity needed) * ([sin v] of (launch angle))) // Adjust for height difference change [initial y velocity v] by ((distance y) / [10])
🎯 Advanced Targeting System
For precise targeting with gravity compensation:
// Advanced ballistics calculator define calculate ballistic trajectory (target x) (target y) // Set physics constants set [gravity v] to [0.5] set [air resistance v] to [0.02] // Calculate basic trajectory set [dx v] to ((target x) - (x position)) set [dy v] to ((target y) - (y position)) // Calculate time to target (horizontal) set [time to target v] to ([abs v] of ((dx) / [15])) // Calculate required vertical velocity with gravity compensation set [required vy v] to (((dy) / (time to target)) + ((gravity) * (time to target) / [2])) // Calculate horizontal velocity set [required vx v] to ((dx) / (time to target)) // Apply calculated velocities set [arrow x velocity v] to (required vx) set [arrow y velocity v] to (required vy) // Launch projectile broadcast [launch arrow v]
🚀 Real-time Projectile System
Complete projectile motion with physics simulation:
// Projectile motion simulation when I receive [launch arrow v] // Initialize projectile go to x: (launcher x) y: (launcher y) set [projectile x v] to (arrow x velocity) set [projectile y v] to (arrow y velocity) set [projectile active v] to [true] // Physics simulation loop repeat until <not <(projectile active) = [true]>> // Update position change x by (projectile x) change y by (projectile y) // Apply gravity change [projectile y v] by ((gravity) * [-1]) // Apply air resistance set [projectile x v] to ((projectile x) * ([1] - (air resistance))) set [projectile y v] to ((projectile y) * ([1] - (air resistance))) // Check for collision if <touching [player v]?> then broadcast [arrow hit v] set [projectile active v] to [false] end // Check for ground collision if <(y position) < [-180]> then broadcast [arrow missed v] set [projectile active v] to [false] end // Visual trail effect create clone of [trail particle v] wait [0.02] seconds end
🎮 Predictive Targeting System
For hitting moving targets with lead calculation:
// Predictive targeting for moving targets define calculate intercept (target x) (target y) (target vx) (target vy) // Get current positions set [shooter x v] to (x position) set [shooter y v] to (y position) // Calculate relative position set [relative x v] to ((target x) - (shooter x)) set [relative y v] to ((target y) - (shooter y)) // Projectile speed (constant) set [projectile speed v] to [20] // Calculate intercept time using quadratic formula set [a v] to (((target vx) * (target vx)) + ((target vy) * (target vy)) - ((projectile speed) * (projectile speed))) set [b v] to ([2] * (((relative x) * (target vx)) + ((relative y) * (target vy)))) set [c v] to (((relative x) * (relative x)) + ((relative y) * (relative y))) // Solve quadratic equation set [discriminant v] to (((b) * (b)) - ([4] * (a) * (c))) if <(discriminant) ≥ [0]> then set [t1 v] to ((([0] - (b)) + ([sqrt v] of (discriminant))) / ([2] * (a))) set [t2 v] to ((([0] - (b)) - ([sqrt v] of (discriminant))) / ([2] * (a))) // Choose positive, smaller time if <<(t1) > [0]> and <<(t2) ≤ [0]> or <(t1) < (t2)>>> then set [intercept time v] to (t1) else set [intercept time v] to (t2) end // Calculate intercept position set [intercept x v] to ((target x) + ((target vx) * (intercept time))) set [intercept y v] to ((target y) + ((target vy) * (intercept time))) // Calculate trajectory to intercept point calculate ballistic trajectory (intercept x) (intercept y) else // No solution - target too fast calculate ballistic trajectory (target x) (target y) end
🎯 Angle-based Targeting Alternative
Simplified approach using angle calculations:
// Simplified angle-based targeting define aim at target (target x) (target y) // Calculate angle to target set [angle to target v] to ([atan2 v] of ((target y) - (y position)) ((target x) - (x position))) // Calculate distance for power adjustment set [distance to target v] to ([sqrt v] of ((((target x) - (x position)) * ((target x) - (x position))) + (((target y) - (y position)) * ((target y) - (y position))))) // Adjust angle for gravity drop (add elevation) set [elevation angle v] to ((angle to target) + ([atan v] of ((distance to target) / [200]))) // Calculate velocity components set [launch power v] to ((distance to target) / [8]) set [arrow x velocity v] to ((launch power) * ([cos v] of (elevation angle))) set [arrow y velocity v] to ((launch power) * ([sin v] of (elevation angle))) // Visual aiming indicator point in direction (elevation angle) set [aiming v] to [true]
🔬 Physics Accuracy Optimization
Fine-tuning for realistic ballistics:
// Physics optimization system define optimize trajectory accuracy // Adaptive time step for precision if <(distance to target) > [300]> then set [physics timestep v] to [0.01] else set [physics timestep v] to [0.02] end // Wind effect simulation set [wind x v] to ((random [-2] to [2]) / [10]) set [wind y v] to ((random [-1] to [1]) / [10]) // Enhanced gravity model set [gravity strength v] to [0.5] if <(y position) > [0]> then // Reduced gravity at height set [effective gravity v] to ((gravity strength) * [0.8]) else set [effective gravity v] to (gravity strength) end // Trajectory correction system if <(distance ([abs v] of ((target x) - (x position)))) > [50]> then // Recalculate trajectory every 30 frames for long shots if <((timer) mod [0.5]) = [0]> then calculate ballistic trajectory (target x) (target y) end end
💎 Pro Tips for Ballistics
- Gravity constant: Start with 0.5 and adjust based on game feel
- Prediction accuracy: Update targeting every few frames, not every frame
- Visual feedback: Show trajectory preview for player understanding
- Performance: Use simplified physics for distant targets
- Realism balance: Perfect accuracy isn’t always fun - add slight randomness
This system gives you Hollywood-level ballistics accuracy! 🎬🎯
PE
PhysicsEngine_Dev
Replied 2 hours later
@BallisticsMath_Expert This is absolutely incredible! 🤯 The predictive targeting system works perfectly!
I implemented the intercept calculation and now my enemies can hit moving targets with scary accuracy. One question - how do I add some randomness to make it feel more natural and less robotic?
GB
GameBalance_Specialist
Replied 1 hour later
@PhysicsEngine_Dev Great question about balancing accuracy! Here’s how to add natural variation:
// Natural accuracy variation system define add shooting variation (accuracy level) // Accuracy level: 1-100 (100 = perfect) set [accuracy factor v] to ((accuracy level) / [100]) // Calculate error range set [max error v] to ([10] * ([1] - (accuracy factor))) // Add random variation to target position set [error x v] to (random ((max error) * [-1]) to (max error)) set [error y v] to (random ((max error) * [-1]) to (max error)) // Apply error to targeting set [adjusted target x v] to ((target x) + (error x)) set [adjusted target y v] to ((target y) + (error y)) // Use adjusted target for calculations calculate ballistic trajectory (adjusted target x) (adjusted target y)
This creates realistic shooting patterns that feel natural! 🎯
VB
Vibelf_Community
Pinned Message • Moderator
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