The calculations above aren't correct. When cells are connected in series (as in the TK70) to make a battery, each cell puts out the the total current drawn.
(It's parallel battery connections that divide up the current.)
On turbo, the TK70 draws as much as 9.5 Amperes, depending on the battery voltage.
So, if under load all 4 cells are measuring a combined potential difference of 3.7 Volts, the current draw of the TK70 would be 9.5 Amperes.
That means each of the 4 cells would be running at 9.5A, (and 0.925 Volts, if all 4 cells are equal).
At 6 Volts on turbo, the TK70 only draws 5A.
So at 6 Volts, the power consumption is 6V*5A=30 Watts.
At 3.7 Volts, the power consumption is 3.7V*9.5A=35 Watts.
However, no D cell currently in existence can maintain 1.5V at 5A draw, so the current would almost certainly run higher than 5A all the time on Turbo due to voltage drop under load.
So with Alkaline cells being what they are at present, there is no way any Alkaline can run the TK70 on Turbo for extended periods, period.
If a very good NiMH D cell can maintain 1.125V under 7.5A load, then the following would apply:
4* D cells @ 1.125V = 4.5V. Draw at 4.5V = 7.5A (per cell).
4.5v*7.5A = 33.75 Watts.
To really make it work better, they'd need to go up to a 6 D cell battery tube so the higher Voltage would mean lower currents could be drawn, and the whole setup would work better. The current 4D setup is really dependent on very good cells in very good condition that can maintain more than 1V under very high current loads.