How do you convert dose and shot volume suggestions for a specific coffee from 58mm to your 49mm espresso machines?

my approach originated from jim schulman's paper on extraction. there he characterizes the puck by the ratio of weight to hole area - which in a cylinder is proportional to the pucks depth. So I started correcting for the smaller area of my 49mm machine with a smaller dose. The ratio of 58mm basket area (26.4cm^2) to area of a 49mm (18.9cm^2) is 1.4. To keep the depth the same, I started dividing the recommended 58mm doses by 1.4. I also aim for a smaller shot weight (or volumes as approximation) by having a slower flow rate. What I want to hold constant by this is:

1. the pucks depth
2. the flow per basket area which equals the average migration velocity (downwards speed). For example a flow of 100ml
per minute and a 58 mm basket can be expressed as 3.8 ml/cm^2/min = 3.8 cm/min

=>1. and 2. determine together the contact time of an imaginary water package travelling through the coffee

3. the total duration of the extraction

[EDIT] ok, the whole idea is essentially useless.. unless for a comparison in the following situation:

1. one specific roasted coffee (including days past roast)
2. same grinder
3. two machines with very similar in their characteristics as for example: pressure regulation (incl. preinfusion/ramp-up time), showerscreen geometry and the depth of the brew chamber with locked in pf (max. puck thickness) ...

welone wrote:my approach originated from jim schulman's paper on extraction. there he characterizes the puck by the ratio of weight to hole area - which in a cylinder is proportional to the pucks depth. So I started correcting for the smaller area of my 49mm machine with a smaller dose. The ratio of 58mm basket area (26.4cm^2) to area of a 49mm (18.9cm^2) is 1.4.

I don't have any answers for you but I think you shoud be careful not to use the area of the bottom of the basket. I think it would be the surface area of the holes in the bottom the basket. That's means counting the number of holes in the bottom of the basket and seeing if the hole diameters are the same.

Thanks for the heads up jeff

that is certainly a valid point when you would want to get really exact numbers. but when comparing for instance the rancilio, gaggia and olympia basket it seems that they are very similar in terms of hole size and number of holes per area.
furthermore in illy's book they claim that the basket bottom contributes almost nothing to the overall resistance of the extraction - this way also comparatively big differences in basket perforation would affect the overall resistance only minimal.

My goal is to get a rough estimation +/- 10% of recommended shot volume and dose conversion factors.