Efficient Calculation of Final Magnitude and Angle in Vector Addition Method

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Discussion Overview

The discussion revolves around methods for calculating the final magnitude and angle in vector addition, particularly in the context of electrical engineering. Participants explore a proposed formula based on Euclid's axioms and discuss its implications and derivations.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant, an electrician, proposes a method for calculating the final magnitude (Lₜ) using the formula ∑(cos(θₙ-θₜ)⋅Lₙ)=Lₜ, expressing a desire to derive a simpler method for calculating the final angle (θₜ).
  • Another participant questions the clarity of the derivation and the absence of θₜ in the final equation, suggesting that the calculation typically involves complex number representations.
  • Some participants express confusion over the proposed method and request clearer steps or examples to understand the application better.
  • There is mention of traditional vector addition methods, such as the compass method and tip-to-tail method, and the challenges faced when using calculators for complex calculations.
  • One participant outlines the process of vector addition in Cartesian coordinates, confirming the correctness of the initial vector definitions and their resultant vector.
  • Another participant inquires about the specific application of the calculations, suggesting it may relate to power factor correction in electrical systems.

Areas of Agreement / Disagreement

Participants express varying levels of understanding and agreement regarding the proposed method. There is no consensus on the validity or clarity of the approach, with multiple competing views on how to effectively calculate the final magnitude and angle in vector addition.

Contextual Notes

Some participants note the limitations of the proposed method, including potential typos and the need for clearer derivations. There is also a recognition that vector addition generally does not have shortcuts unless specific relationships exist between the vectors.

Who May Find This Useful

This discussion may be useful for electricians, electrical engineers, and students interested in vector addition methods, particularly in the context of electrical systems and calculations involving angles and magnitudes.

  • #31
okay this is what I can get one my own

$$ \left( \sum (L_n cos(\theta_n - \theta_t)) \right)^2 = \left( \sum (L_n sin (\theta_n)) \right)^2 + \left( \sum (L_n cos(\theta_n)) \right)^2 $$

$$ \left( \sum (L_n cos(\theta_n - \theta_t)) \right)^2 / \left( \sum (L_n) \right)^2 = \left( \left( \sum (L_n sin (\theta_n)) \right)^2 + \left( \sum (L_n cos(\theta_n)) \right)^2 \right) / \left( \sum (L_n) \right)^2 $$

$$ \left( \sum (cos(\theta_n) cos(\theta_t) + sin(\theta_n) sin(\theta_t)) \right)^2 = \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 $$

$$ \left( \sum (cos(\theta_n) cos(\theta_t)) + \sum (sin(\theta_n) sin(\theta_t)) \right)^2 = \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 $$

$$ \left( cos(\theta_t) \sum (cos(\theta_n)) + sin(\theta_t) \sum (sin(\theta_n)) \right)^2 = \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 $$

$$ \left( cos(\theta_t) \sum (cos(\theta_n)) \right)^2 +2 cos(\theta_t) \sum (cos(\theta_n)) sin(\theta_t) \sum (sin(\theta_n)) + \left( sin(\theta_t) \sum (sin(\theta_n)) \right)^2 = \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 $$
 
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  • #32
$$ \left( \left( cos(\theta_t) \sum (cos(\theta_n)) \right)^2 +2 cos(\theta_t) \sum (cos(\theta_n)) sin(\theta_t) \sum (sin(\theta_n)) + \left( sin(\theta_t) \sum (sin(\theta_n)) \right)^2 \right) / \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) = \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) / \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) $$

$$ \left( \left( cos(\theta_t) \sum (cos(\theta_n)) \right)^2 \right) / \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) + \left( 2 cos(\theta_t) \sum (cos(\theta_n)) sin(\theta_t) \sum (sin(\theta_n)) \right) / \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) + \left( \left( sin(\theta_t) \sum (sin(\theta_n)) \right)^2 \right) / \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) = 1 $$

$$ \left( cos(\theta_t) \right)^2 / \left( \left( \sum (sin (\theta_n)) \right)^2 + 1 \right) + \left( 2 cos(\theta_t) sin(\theta_t) \right) / \left( \left( \sum (sin (\theta_n)) \right) + \left( \sum (cos(\theta_n)) \right) \right) + \left( sin(\theta_t) \right)^2 / \left( 1 + \left( \sum (cos(\theta_n)) \right)^2 \right) = 1 $$
 
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  • #33
$$ \left( \left( cos(\theta_t) \sum (cos(\theta_n)) \right)^2 + 2 cos(\theta_t) \sum (cos(\theta_n)) sin(\theta_t) \sum (sin(\theta_n)) + \left( sin(\theta_t) \sum (sin(\theta_n)) \right)^2 \right) / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) = \left( \left( \sum (sin (\theta_n)) \right)^2 + \left( \sum (cos(\theta_n)) \right)^2 \right) / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) $$

$$ \left( \left( cos(\theta_t) \sum (cos(\theta_n)) \right)^2 \right) / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) + \left( 2 cos(\theta_t) \sum (cos(\theta_n)) sin(\theta_t) \sum (sin(\theta_n)) \right) / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) + \left( \left( sin(\theta_t) \sum (sin(\theta_n)) \right)^2 \right) / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) = \left( \sum (sin (\theta_n)) \right)^2 / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) + \left( \sum (cos(\theta_n)) \right)^2 / \left( \sum (sin (\theta_n)) \sum (cos(\theta_n)) \right) $$

$$ \left( cos(\theta_t) \right)^2 \sum (cot(\theta_n)) + 2 cos(\theta_t) sin(\theta_t) + \left( sin(\theta_t) \right)^2 \sum (tan(\theta_n)) = \sum (tan (\theta_n)) + \sum (cot(\theta_n)) $$
 
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  • #34
found an error in my equation, this is fixed

$$ \frac {\left( cos(\theta_t) \sum (L_n cos(\theta_n)) \right)^2 + 2 cos(\theta_t) \sum (L_n cos(\theta_n)) sin(\theta_t) \sum (L_n sin(\theta_n)) + \left( sin(\theta_t) \sum (L_n sin(\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} = \frac {\left( \sum (L_n sin (\theta_n)) \right)^2 + \left( \sum (L_n cos(\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} $$

$$ \frac {\left( cos(\theta_t) \sum (L_n cos(\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} + \frac {2 cos(\theta_t) \sum (L_n cos(\theta_n)) sin(\theta_t) \sum (L_n sin(\theta_n))} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} + \frac {\left( sin(\theta_t) \sum (L_n sin(\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} = \frac {\left( \sum (L_n sin (\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} + \frac {\left( \sum (L_n cos(\theta_n)) \right)^2} {\sum (L_n sin (\theta_n)) \sum (L_n cos(\theta_n))} $$

$$ cos ^2 (\theta_t) \frac {\sum L_n cos(\theta_n)} {\sum L_n sin (\theta_n)} + 2 cos(\theta_t) sin(\theta_t) + sin ^2 (\theta_t) \frac {\sum L_n sin(\theta_n)} {\sum L_n cos(\theta_n)} = \frac {\sum L_n sin (\theta_n)} {\sum L_n cos(\theta_n)} + \frac {\sum L_n cos(\theta_n)} {\sum L_n sin (\theta_n)} $$
 
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