I would suggest that you do some rough calculations of the forces involved. You can estimate the force required to hold a cable up with a given amount of sag by using the on-line calculator athttp://www.spaceagecontrol.com/calccabl.htm?F=100&a=500&q=.02&g=32.1850393&Submit+Button=Calculate
Example: For #12 hard drawn bare copper (20 lb/1000ft), you would need 71 lbs of tension to hold up 535 ft of wire. But this doesn't include anything attached to the center of the antenna. For every lb you add there, assuming a 10 ft sag, you would have to increase the tension by 13.4 lbs. (Easy geometry calculation for a rough approximation). If you allow only 5 ft sag, this number increases to 26.8 lbs tension for every lb you add at the center. If you have a 50 ft mast with guys anchored at 50 ft away, the vertical load on the mast would be the same as the tension in the wire (another easy geometry calculation). So with a 10 ft sag, if 40 ft of your homemade ladder line weighs 4 lbs (it sounds heavy), the tension required would be 54 + 71 = 125 lbs. (WIK's seat of the pants guess was very good, but he probably forgot about the next item).
Now you need to calculate wind loading. If you look at http://www.vk1od.net/rigging/sag.htm
you will see that hard drawn copper is probably not a good choice. It breaks at about 200 lbs. Copperweld would be a much better choice. Its stronger and a little lighter. Then you can look at the example at http://www.iaei.org/subscriber/magazine/02_c/other_code.htm
for load calculations due to wind. From this you will discover that for a 70 mph wind (not considering gusts) that the additional loading on the 3.6 sq ft of wire is 45 lbs. Since this is distributed linearly, just go back and add it to the wire weight and plug it back into the calculator referenced above to get an approximation of the load. That will give you a tension of 370 lbs for a 10 ft sag. Now we are almost done, but we have to add something for wind loading on the ladder line. Not knowing what this looks like, but making an estimate based on the size of your spacers, 40 ft comes out to be about 1.5 sq ft, or a wind load of 18.8 lbs at 70 mph. If you assume half of that is supported from below, that adds 9.4 lbs to the antenna. Since that is at the center of the element it get multiplied by 13.4, so it adds 126 lbs of tension. We now have a final answer of 370 + 126 = 496 lbs for 70 mph wind. That's 70% of the breaking strength of #12 copperweld, so maybe you need a larger wire and repeat the calculations. It's more than any simple mast can handle too, so maybe another plan of attack is in order. You could allow a much larger sag which will reduce the forces involved, but the antenna will be getting very low in the center. Maybe three supports? Inverted vee? Shorter antenna?