You can climb at Vx, Vy, and VCC - Cruise climb (Vcc - “enroute climb speed”). The cruise climb for most of GA single engines is about +16 knots to Vy. The 172’s sea-level Vy is published at 74 knots. Enroute climb (Vcc) is published at 75-85 knots. The task is not to overheat your engine and/or to save as much fuel as you can. Vertical climb depends on your weight and altitude/temperature (pressure altitude). In cruise climb, I lean mixture for the best climb on Vy or VCC but within temperature limits, C-172 with NGX is good for this as she has an assistance regime for leaning, and my best climb - vertical speed is always different. Normal enroute climbs are performed with flaps up and full throttle and at speeds 5 to 10 knots higher than best rate-of-climb speeds for the best combination of performance, visibility, and engine cooling.
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