New math, old math, unusual loads dispatched at non-standard routing times... all I know is, a 500 mile run takes about 8 hours to run, 650 miles is about 10.5 hours, 750 miles is 12 hours. Longer loads and you can start doubling up and figure from there. Then figure 15 minutes per fuel stop. (Yes, there are exceptions to these figures, there always are exceptions to everything, but generally speaking this is what it is.)
On all loads longer than 500 miles you want to be able to deliver it two hours early. A two hour window allows time for construction and other traffic delays, bad weather, missing an exit or taking a wrong turn, most can change a flat tire in an hour. On loads less than 500 miles a two hour windows isn't practical or necessary.
On loads that require a 5 hour break, you need to be able to build up enough time for the 5 hour break, plus that two hour window, otherwise you're cutting things too close and any of the above delays could make you late. A 950 mile run can be done in under 16 hours, but your 16 hour clock needs to start when you leave the shipper, not a minute sooner. Loads between 950 miles and 1300 miles are the sweet spot where they really and truly need to be swapped, because you cannot run those and take a 5 hour break and be on a pace to deliver the load two hours early. Loads greater than 1300 miles can comfortably be delivered with a 5 hour break and a two hour window.
Example, a 1200 mile run at 47 MPH is 25.53 hours. General rule of thumb is to add 15 minutes to the time for getting loaded, and then round up to the next half hour, so this load will generally be dispatched at 26 hours. Using the "650 miles @ 10.5 hours" guide above (double it and take off 100 miles and 2 hours), and that 1200 miles is going to take roughly 19 hours to run. Add 5 hours for the break and you're at 24 hours, which leaves the two hour window... except, you'll need to whack off 30 minutes for two fuel stops, leaving you one and a half hours to spare. If you need 3 fuel stops you're down to an hour and 15 minutes. That's a pretty tiny window to shoot for and leaves little room for error.
1250 miles and you really can get those two hours in, but it depends on routing, time of day, and other factors. At 1300 miles you can pretty much count on running that one comfortably, safely, and without much stress, getting the 5 hour break in and having a two hour window to play with if you need it.
You can disagree if you like, and you can go all "Ironman" all you want, but the above is reality for a professional cargo van driver. Again, yes, I know there are exceptions, but they are just that, exceptions, and not the norm. It's the people who think they are the Ironman exception to the norm who run between 950 and 1300 miles with no break that should scare the Hеll out of everyone on the road. Yes, it is a proven fact that most accidents happen in the first couple hours of service, but that data is garnered from truckers who have to log HoS and does not even include a data sampling base for those driving more than 11 or 12 hours.
Everybody is a good driver. Just ask them and they'll tell you. "I'm an excellent driver. Never had an accident, therefore I'm an excellent driver. Yeah. Yeah." They're all Rainman. Drunks will tell you they're not too drunk to drive, and tired and fatigued people will tell you they are neither tired nor fatigued.
The DOT doesn't have statistics on the accident rate beyond about 12 hours, but carriers with cargo vans who keep track of such things do. I've discussed it with those who keep track of these things, and seen the numbers from two different carriers (my former and my current carrier), and the numbers show, unambiguously, that the rate of cargo van accidents and incidents rises after a certain number of miles or hours between breaks.
Con-Way NOW, my former carrier would rarely let a cargo van go more than 750 or 800 miles without a swap unless there was ample time in the load for breaks. Panther, my current carrier, is a little more lenient with 900 miles or 16 hours, whichever comes first. Granted, Panther applies the rule hard and fast and uses no intelligence or common sense whatsoever in the decision making process, as they prefer to use theoretical worst-case scenarios, rather than the reality above, in determining how far someone can drive in a given amount of time. They aren't as interested in reducing the probability of a load being delivered late, they much prefer to eliminate the possibility of it being late, and in doing so they make some truly stupid decisions (like paying $300 for a cross-dock fee at a tow yard in the middle of the night on a load that doesn't even need to be swapped in the first place). But I digress.
Don't be stupid. It's not whether or not you can do something, but rather whether or not you should. Don't let a Dollar Sign Woody drain the blood from your brain and make you stupid. You have to pick up and deliver Safely, Legally, and On-Time. Gotta have all three all the time.