The Munter rate ( of the famed Swiss guide Werner Munter e.g. Munter knot, evolution of avalanche decision making models etc) is a more precise method of the classic time estimator of ~3km and 300m or 1000′ per hr for class 1 and 2 hiking/running/skiing terrain.
TIME = (DISTANCE (km) + ELEVATION (m)/100))/rate
It is unitless, with the basic default rates being:
uphill travel on foot or skis – 4
flat or downhill on foot – 6
downhill on skis – 10
bushwhacking – 2
BCA has a good summary here: https://backcountryaccess.com/how-to-calculate-backcountry-touring-time-based-distance-elevation-gain/
https://www.appliedalpinism.com/guide-pace makes a nice little app, though only one segment at at time.
I have a spreadsheet set up where I use google earth to map out the legs and put in the km and meter inputs in.
I see Munter rate much like heart rate tracking: I did lots at the beginning and as I learnt to estimate better I only use them for critical events or to re-calibrate.
When calibrating my Munter rates I used TP to select portions of a route, grab the numbers (km, time, meters) and solve for rate. I tweaked my rates for several grade classes of uphill , footwear (e.g. running shoes vs mountain boots), and nature of trail (e.g. breaking trail in snow vs following skin track or hard surface; or loose scree or blocky talus vs good trail). I found with these rates tuned I could estimate a 5-7 hr day down to minutes for each segment.
As a TP tool, it would help with tuning rates for estimation, or I think it would a useful way to have an ‘integrated’ travel rate that brought together horizontal and vertical elements over different terrain technicalities.
Marc Chavin also has a similar approach for class 3/4 terrain:
time = (distance x 1000 + elevation) x rate / 60
As a working husband and parent of two children being able to accurately tell my wife how long I will be on my 5am sunday morning mountain explore, or choosing a feasible route, is critical to happy family dynamics!