Reading the RAF link above it seems to have been developed from a precursor to the Boeing 707.
Tim, when you say it's uncomfortable, is that because of its construction - all metal, stiff winged - or simply because it is cramped due to the narrow fuselage?
It's because having a joint riveted bloody hurts. I have experience. But it's not actually a reference to the aircraft!
Yes, the C135 is a precursor to the B707. It was developed for the civil market, but was regarded as too small by the potential customers. Boeing went away and redesigned it, but in the meantime the USAF bought it in huge numbers as a transport and tanker aircraft.Since then, it's been expanded into a number of roles. Note, the E3 Sentry is based on the B707, not the C135, and the difference in size is significant but the family resemblance obvious.
Edit: the poster of the flypast participants
looks as if it's to scale, but it isn't. The RC135 is 135ft long, the E3 is 153ft, and the A330 is 193ft long (and the weights are 146 tonnes, 156 tonnes and 233 tonnes).