Willen, the formula 492/f[MHz] is good, but is half wave in feet, no inch. (in meter 150/f[MHz]).
half wave for 91 MHz = 492 / 91= 5.4066 feet = 64.88 inchs = 1.65 m (only two digits is good for decimals in this case). (1 foot = 12 inch, 1 foot= 0.0254 m)
1/2Wave / diameter = 64.88 / (1.8 cm / 2.54) = 91.55 ==> k = 0.961 in the graph of the ....freeserver....
In my graph, Full Wave/d ~ 183.15 ==> k = 0.965, L = 62.35", for k=0.965, L = 62.60", for k= 0.941, L= 61.05". The diference between lenghts for the k is only 2.4% (of half wave)
View attachment 66577
In VHF antenna engineering an error of 3% is good!
The problems are:
1) 492 (in feet) and 150 (meters) is a aproximation for half speed of light.
2) The factor k is for resonance of the dipole. An exact THIN half wave dipole has Z=73.1 + j42.5 Ohms. For resonance, you need X=0, then Z= 73.1+j0 Ohms. For X= 0, you need lenght less than half wave, for that, you includes the factor k and this depends on the diameter. See wikipedia, dipole.
For reactance calculation are aproximations (with several methods). According to the method the value of k is different.
3) That formula is for dipole in free space (theoric value). When you put a dipole on earth, the impedance Z varies with the height, and then, you have Reactance and Resistance different than the free space impedance, and then, you need adjust the lenght for X=0.
4) But, with a tube of 1.8 cm in 91 MHz, you have more or less BW= 3.0 MHz for SWR = 1.5 ( 89.5 MHz < fzero < 92.5 MHz). Is a great BW ! Your dipole, more or less, will have a resistance of 75 Ohms, What cable will use? 50 Ohms (RG213). Your SWR ~ 1.4. If the cable is short not problem, but if your feeder is long, you need adjust the impedance with a gamma match (for example), for avoid excessives losses.
Best regards.
Nestor