Projectile Arrow Angle Transformation Equation

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Discussion Overview

The discussion revolves around the mathematical modeling of an arrow's flight in an archery game, specifically focusing on how to transform the arrow's angle during its trajectory to mimic realistic behavior. Participants explore the projectile motion equations and seek to understand how to represent the arrow's orientation based on its velocity vector.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant describes the need for an equation to calculate the transformation of the arrow's angle during flight, based on initial conditions such as angle, speed, distance, and time.
  • The same participant provides initial equations for the x and y components of projectile motion, indicating a desire to replicate the arrow falling tip downwards regardless of the launch angle.
  • Another participant states that the arrow points in the direction of its velocity vector, implying that the orientation is tied to the arrow's motion rather than a fixed angle.
  • A request for clarification on the concept of the velocity vector is made, seeking a mathematical expression or explanation.
  • A subsequent response questions the understanding of vectors, suggesting a need for foundational knowledge in vector mathematics.

Areas of Agreement / Disagreement

Participants have not reached a consensus on how to mathematically represent the arrow's angle transformation. There is a mix of understanding regarding the concept of velocity vectors and their implications for the arrow's orientation during flight.

Contextual Notes

The discussion includes assumptions about the physics of projectile motion and the representation of vectors, which may not be fully articulated or agreed upon by all participants.

saad749
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I have an Archery game. I am firing the arrow with the projectile equation. I need the arrow to transform it angle during the flight as happens in real life. (For Example When Firing the Arrow at 90 degrees the Arrow should return with its head pointing straight to the ground and similarly for other angles). Is there any generic equation to calculate the transformation of the angle based on the initial angle, initial speed(x/y components), distance, time etc.

x = (Vi * Math.cos(Initial Angle) * t)+ 75; // Vix * t
y = ((Vi * Math.sin(Initial Angle) * t) - (0.5 * 10 * t * t)); // Viy * t - (0.5 * g * t^2)

A Example of what type of transformation I need : link deleted

In the above game the arrow always falls tip downwards no matter what the initial angle and velocity. I have to replicate this.

I am not a physics guy, so might be missing something very unreasonable and am implementing this game in Javascript :P
 
Last edited by a moderator:
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Arrow just points in the direction of its velocity vector.
 
Would u please explain what do u mean by vector of its velocity? or can u express it mathematically? Thanks.
 

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