It seems this comes up again and again.

There are two sources of vacuum "loss" in sap ladders. First is the friction drop caused by flow of the liquid and gas. Second is the column of liquid.

The intent of sap ladders is to reduce the loss caused by the column of liquid. To do this you must have air/gas flowing in the system. For example, if you have a 10 foot ladder with no air/gas, you have a "solid" column of liquid and this column will cause a vacuum loss equivalent to 10 feet of liquid--about 10 inches of vacuum. However, if for example, the average column content is half gas and half liquid, the liquid column is only 5 feet high, and the loss is only 5 feet of liquid--about 5 inches of mercury.

But if the flow of liquid is fixed, adding gas increases the velocity of the liquid and this increases the friction loss.

Finally, if you are adding air, there will be an effect on the vacuum pump, which depends on the capacity and characteristic curve of the pump.

All this suggests that there will be an optimum quantity of gas/air, and you will have to find that optimum by experiment. Note that the optimum will depend on the quantity of liquid flowing.

The friction loss can be reduced by increasing the cross section of the ladder, which reduces the fluid velocity. However, as the cross section increases there is a tendency for the gas/air to "slip" past the liquid, causing the liquid quantity in the ladder to increase and thus increase the vacuum loss. There is very little slip in 5/16 in tubing, but slip increases rapidly in larger pipe/tube.

Lots of things to think about and diddle to reach an optimum.