Hydraulic properties of channels and cross sections are computed differently in HECHMS and HEC1.
General Channel Properties
In HECHMS, properties are computed from the physical properties of the channel, whereas in HEC1 the properties are computed with formulas based on the kinematic wave assumption. In HECHMS the crosssectional flow area is computed as:
and the ratio of wave speed, c, to flow velocity, v, is:

\frac{c}{v} = \frac{(10wzy)+(16zy^2 \sqrt{z^2+1})+(5w^2)+(6wy\sqrt{z^2+1})}{3(w+2zy)(w+2y \sqrt{z^2+1})}

where w is the bottom width, z is the side slope, and y is the flow depth. Velocity is computed using Manning's formula and the properties of the cross section.
In HEC1 the crosssectional flow area is computed as:

A=(\frac{Q}{\alpha})^\frac{1}{m} 
and the wave speed, c, is computed as:
where \alpha and m are kinematic parameters based on the channel shape.
Eight Point Cross Sections
In HECHMS the flow depth for a given discharge is determined from the cross section properties and then area, top width, and wave speed are computed for that depth using the cross section properties. In HEC1 the discharge, area, top width, and wave speed are computed for 20 depths and stored in a table. During the routing process, area, top width, and wave speed were interpolated from the table for each discharge value. HECHMS guarantees that the area, top width, and wave speed are computed exactly for each discharge value.