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Determining the length of a driven element


During a casual conversation recently, the topic of aerial trimming came up. 
Perhaps this may be a little off-topic here but since I don't know the answer 
I thought this would be a good place to ask anyway.

Say a dipole has an SWR of 5:1 at one end of a band and 4:1 at the other end. 
Further, let's say that the dipole will be used at the centre of the band and 
with a reasonable SWR. It has been determined that the dipole needs to be 
shortened. The question is by how much?

The person asking the question is reluctant to pull the aerial down a dozen 
times so that short lengths can be nibbled off each end and instead wants to 
know if the amount that needs to be cut off can be determined from the 
difference in the SWR at both ends of the band.

A logical question I suppose but is there a reasonable answer?

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