Terminal velocity is reached when the force on the rider due to gravitation acceleration equals the force from aerodynamic drag on the rider and bicycle plus rolling resistance of the bicycle.
In the calculation below I will assume rolling resistance of the bicycle is much less than the air drag and will omit it. I may update this later. I will use typical values for gravity, air density etc at sea level on Planet Earth.
Gravitational force on the rider and bike F = m × g × sin(ϕ)
- m is mass of rider and bike 80kg for rider 10kg for bike is 90kg
- g is gravitational acceleration 9.81 m/s²
- ϕ is the slope in radians, 19° is 0.33 radians
That yields a force of approx. 287.4 Newtons
Aerodynamic drag force is CdA × ρ × v² / 2
- CdA is drag coefficient × frontal area, I'll use a figure of 0.275 from the page linked to by the OP.
- ρ is air density 1.225 kg/m²
- v is velocity.
Terminal velocity is therefore √ ( 2 F / ( CdA × ρ ) ) which yields 41.3 m/s or about 149 km/h, 92.5 mph.