I think the minimum viable aerial is about 20cm or so at 1/16th of a full wavelength to still get most stations. The shark fins on some cars are normally active aerials and require a power supply (like most DAB aerials) so the super folded or coiled bee sting types may well be similar to be effective.
For a simple monopole aerial:
FM (Wavelength(Lambda) = Speed of Light(m/s) / Frequency(Hz))
Bottom of freq range
1 Wavelength = 3*10^8 / 87.5*10^6 = 3.4 meters.
So 1/4 wave = 86cm
Top of freq range
1 Wavelength = 3*10^8 / 108*10^6 = 2.8 meters.
So 1/4 wave = 69.4cm
For mid range 300 / 97.8 = 3.07 meters.
So 1/2, 1/4 , 1/8, 1/16, 1/32, 1/64 = 1.53m, 76.7cm, 38.3cm, 19.2cm, 9.6cm, 4.8cm etc.
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TG