How to find the right number of elements for an array?

Hi friends,
MY AUDIENCE AREA ((DEEPTH 100FT,WIIDTH
80/2= 40 FT ,FAR 2.50,COV ANG 47DEEGRE)).
I DO NOT WANT TO USED ANY DELAY SPEAKER.
I WANT USE ON MAIN TO LINE ARRAY.
MY QUESTION IS HOW TO DO CALCULATE WHAT QUANTITY OF LINE ARRAY NEED ON MY THIS AUDIENCE AEREA ?

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blob:https://school.sounddesignlive.com/1d93bdcb-17d5-48ad-b9f6-010f6a0a1b7e

Hey Saikat, I updated your post title. I hope that's ok.
I'm not sure what these blobs are. They just take me to 404 errors. Maybe you tried to upload a design or an image? What are they supposed to be?

The easy lazy way is to just put your array into a model, run automatic aim and splay, and see if it covers the entire audience.

Otherwise, the minimum number of line array elements is defined by your target coverage angle and your speaker's maximum splay. This is from Bob McCarthy's book.

**Asymmetric composite coupled point source design procedure (Figs.11.17 to 11.18) **

1. Define target top and bottom (VTOP and VBOT) as angle and range (e.g. -5° @20 m).

2. Define the target shape from VTOP to VBOT as coverage angle and range ratio (e.g. 30° @2:1).

3. Define maximum splay (depends on element) and minimum (max/range ratio).

4. Calculate the average splay angle ((max + min)/2), e.g. (10° + 5°)/2 = 7.5°.

5. Calculate minimum element quantity (target coverage angle/average splay).

6. Subdivide the array into composite segments with splay ratios scaled to the shape.

McCarthy, Bob. Sound Systems: Design and Optimization: Modern Techniques and Tools for Sound System Design and Alignment (p. 341). Taylor and Francis. Kindle Edition.