As it's originally presented, there are too many 'unknowns' and assumptions for a definite answer. In a 'best case' situation, the SWR seen at the transmitter end would be dealing primarily with the losses in the feed line. In a 'worst case' situation, the resulting SWR measured in the same place is the result of both feed line losses and impedance mismatches. That opens the door to an almost infinite range of possibilities. (No, it isn't really an 'infinite range', but it is quite 'broad'.)
- 'Doc
No argument with some of this, we are talking about a lot of loss, weather it is bob85's calculation of 5 dB or either of the data sheets I looked up, which are even higher, we are talking about a 68% to 73% signal loss even before the signal gets to the SWR meter at the antenna. However, just because there are high losses does not mean you cannot calculate the SWR at the antenna itself from a reading at the radio end.
The hardest part to achieve this has been getting the loss characteristics of the feedline. Some of us have equipment that can measure this, unfortunately that equipment doesn't do me any good in a hypothetical situation as was presented so I have to resort to what information I can find, I used data sheets for 30 MHz, which in and of them selves will have a margin for error when dealing with 27 MHz.
However, once you have this information it is a matter of picking an arbitrary number to use for the forward power (it doesn't matter what it is as SWR does not change with power, I like to use 100), then calculate the reflected power based on that and the SWR reading you have.
Once you have the effective forward and reflected powers in watts for one side of the feedline it is simply a matter of factoring in loss from the forward signal and gain for the reflected signal to get the forward and reflected power figures at the antenna end, then convert these back into an SWR.
Unless you have so much feed line loss that your SWR meter shows 1:1 at your end you can figure out the readings on the far end.
Now, if the nearby reading was 1:1 I would have agreed with you, not enough information.
The biggest potential problem I see here is most SWR meters aren't exactly the most accurate devices in the world as most read lower than the actual SWR. When dealing with SWR in these conditions the difference from a bad reading is greater on the far end.
The next biggest issue at hand, assuming you don't have fancy equipment that can measure feedline loss directly, is getting accurate loss measurements for a given feedline as sources such as data sheets don't always agree, or provide information at the specific frequency of operation, and even if they do there is always a margin for error in the real thing. These factors also skews the results in the real world.
Even accounting for both of these potential problems, you can still calculate the antennas's SWR to within a reasonable margin of error.
I guess in the end it all has to do with a proper understanding of the language of transmission lines.
The DB