The "cone thing" - usually called a drogue or "basket" serves several purposes ...
1) having aerodynamic fabric "slots" it stabilises in the airflow, so the receiveing pilot is not chasing a moving target
2) it gives a larger "target" for the receiving pilot to see
3) if the receiving pilot is slightly off it guides the probe into the fuel valve 3) At night it is lit so the receiving pilot can actually see a target,
4) the outer thick edge is fabric covered so if the receiving pilot "misses" then no damage is done (if there was nowt but the metal valve the probe could be damaged)
5) no matter how good a "shot" the receiving pilot is, it ensures the probe enters the fuel valve correctly aligned ... other wise there would be a risk of an "offset" connection which might jam.
Having both received and dispensed fuel in the C130 it is a very well tried and tested system that works.
The yellow "bands" on the hose indicate how far out it is trailed ... once connected you actually have to "push" it back in before the valve opens and fuel flows, if you slide back out too far the fuel shuts off BEFORE you reach the maximum extension and disconnect
Regarding 1) above .. I have been on board trying to refuel from a damaged basket that was all over the place ... not fun and getting pretty worried until the skipper finally made contact. This was not a training exercise .. it was "for real" and if he hadn't made contact we would have got very wet ......
Edit
Refuelling from a VC10 ... pre-contact position
In contact.. you can see how the hose has been "pushed in" to the central thick bands ...
