What would the profile “look like”? Well, if you were to graph it, it would be very, very long and skinny... (there is a reason why vertical scales are typically exaggerated)
That might sound snarky, and I know you think you put a lot of thought into the careful wording of your question, but it is very broad as stated: What are you really looking for in an answer, the general appearance of the profile when plotted with vertical and horizontal scales equal? The climb or descent gradients expressed in degrees? Or rise/run slope? What units of measure would you like the answer to be in?
And what is a “typical” flight? (2 hours of cruise, or 12 hours of cruise?!)
I know you said you don't want to crunch actual data, but I think the suggestions here are sound if you are looking for typical. Any effects of wind will average themselves out as you increase your sample size. And there are other variables that have as much or more effect on the climb gradient.
However, if you are looking for a ballpark answer, here is my shot at giving you some additional perspective:
Climb - Airliners don’t typically target a vertical speed in the climb because doing so will cause airspeed to gradually decay. Instead, a climb airspeed is set, making the vertical speed a continuously changing variable. And that vertical speed will vary depending on aircraft type, the load, and whether a fuel efficient cruise climb is chosen, or a higher performance climb rate for terrain clearance. (so again, no such thing as “typical”…)
Cruise - Get a long piece of graph paper because "the altitude profile plotted against distance" for 4 hours at 300 knots at 30,000 feet will be 243 horizontal units for every vertical unit. (This is obviously just an example, you may scale appropriately depending on altitude and duration of flight)
Descent - This is probably easiest to define/predict for “typical”, and there are a few different ways to figure out what a descent profile might look like:
- Vertical speed: For passenger comfort the flight might target 1500-2000 FPM down depending on airspeed and altitude. At 250 knots, (speed limit below 10,000’) and 1500-2000 FPM rate of descent, the gradient would equate to 13-17 units horizontally for every unit vertically.
- The Flight Management System may be programmed to calculate a default 3 degree descent for the autopilot to follow, and most approaches are about 3 degrees. So, 3 degrees is probably a good descent angle to use for typical.
- The Flight Management System on larger airliners typically calculates a descent based on a descent speed profile, which then results in a varying descent angle and vertical speed, just the climb section described above.
- Finally, for rough planning pilots us a 3:1 rule of thumb for descents. This means that for every 3 nautical miles you should plan to lose 1000 feet. This equates to a ratio of about 18 horizontal units for every vertical unit.
I hope this helps.