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My thoughts are that it would be negligible – I think most rads are run with water below the absolute max level and the position (height) of the overflow on different rads probably varies by more that the difference in water level with angle.
My suggestion to confirm this is as follows:
Hold the rad with the filler vertical and the hoses blocked off. Fill up to the overflow using a measuring jug so you know the volume you have put in. Tilt the rad to the angle the filler will be when fitted and measure the volume that comes out of the overflow. My expectation is that this is going to be a relatively small percentage of the total and remember that there is also volume in the engine as well.
If you do this, let us know what the percentage is just for the record.
As a professional engineer (but not, I emphasise, one that has anything to do with engines or motor transport) I would expect a “design margin” of several tens of percent to allow for partially filled rads in normal operation. FYI, pressure piping codes allow operating pressures of up to 72% of design, hence there is a 39% difference between the normal operating level and the max ‘design’ (and then the max design is is well below the ultimate strength – we test to 1.5 times ‘design’ to proove the system). This is typical of the design margins engineers use.
Also remember that the cooling duty for the rad when riding the roads of S W France is a lot less than trying to ride through London traffic.
All the best,