My company has all of our frames and files set up to use British National Grid as the projection. However, when adding in basemaps such as google imagery it becomes painfully slow and virtually unusable. After some tweaking I found that changing the data frames projection to "WGS_1984_Web_Mercator_Auxiliary_Sphere" this solves the slow loading issue, it all becomes super quick.
I have begun to use "WGS_1984_Web_Mercator_Auxiliary_Sphere" however it appears to be scaling wrong? I have measured a distance on the same map, one with BNG and one with "WGS_1984_Web_Mercator_Auxiliary_Sphere" and both give drastically different distances. Have I not set transformation correctly? How do I do this?
Which application are you using? Please note that in your question and its tags.
You should read this blog post about why you shouldn't measure distances or areas in the Web Mercator projection.