>>And in some cases there are both straight and automatic air on a car, using a check valve between the control valve and piston/cylinder…<<
My understanding is that's not how it works on the Durango & Silverton. They don't use a check valve between the control valve and piston/cylinder.
Instead, the exhaust from the control valve can selectively either go out through the retainers, as is usual. Or you can select for the exhaust to go through the straight air train line. In the locomotive, you can selectively connect or disconnect the independent brake from the straight air train line. If everything is selected for the straight air train line, and if the automatic brakes are released by increasing or maintaining pressure in the automatic train line, then the brake piston/cylinders will respond to the condition of the independent brake through the straight air line. If the independent brake is released while the automatic brakes are released, all of the exhaust air from the piston/cylinders will go out through the straight air train line to the locomotive and out through the independent brake exhaust. If the independent brake is applied while the automatic brake is released, air will go through the straight air line to the brake piston/cylinder and apply the brakes via straight air.
When the automatic brake is set by reducing the pressure in the automatic brake train line, the control valve disconnects the piston/cylinder from the straight air line (or retainer) altogether. Instead, the control valve will direct air from either the service reservoir or the emergency reservoir to the piston/cylinder, depending on how fast the pressure is reduced in the automatic brake train line. There is some kind of timing mechanism, and if the pressure drops suddenly, the air from the emergency reservoir goes into the piston/cylinder. If it is a more gradual reduction in the automatic line, air from the service reservoir goes into the piston cylinder, the amount depending on the amount of automatic train line air reduction. When the automatic train line pressure is increased, the service or emergency reservoir is disconnected from the piston/cylinder, and the piston/cylinder goes back to being connected to the straight air line.
There's no check valve of the type referred to.
I wonder if the ex-White Pass & Yukon locos will have the same setup as the steam engines, and allow the independent brake to be connected to the straight air line?
Robert