Floating car method: flow, journey and running speed

In the floating car (moving observer) method, for each direction the flow is $q = \dfrac{n_a + y}{t_a + t_w}$ where $n_a$ = vehicles met while running against the stream (in PCU), $y$ = vehicles overtaking the test car minus vehicles overtaken by it during the run with the stream, $t_w$ = journey time with the stream and $t_a$ = journey time against the stream. The mean stream journey time is $\bar t = t_w - y/q$.

Data treatment: PCU factors car 1, bus 2, truck 3 are applied to the opposing counts ($n_a$ = cars + 2 buses + 3 trucks). Overtaking and overtaken counts are used as numbers of vehicles (types are not given). Section length $L = 25.5$ km as given. Times are converted to seconds.

Data per trip (journey time, stopped delay in s; opposing in PCU)

Flow in the N-S direction

The vehicles met on the S-N trips form the N-S stream. Averages over 6 trips: $n_a = 35.67$ PCU, $t_a = 4.336$ min, $t_w = 4.381$ min, $y = 1.00$.

$$q_{NS} = \frac{n_a + y}{t_a + t_w} = \frac{35.67 + 1.00}{4.336 + 4.381} = 4.21\ \text{veh/min} = 252\ \text{veh/h}$$

Flow in the S-N direction

Averages: $n_a = 37.00$ PCU, $t_a = 4.381$ min, $t_w = 4.336$ min, $y = 0.83$.

$$q_{SN} = \frac{37.00 + 0.83}{4.381 + 4.336} = 4.34\ \text{veh/min} = 260\ \text{veh/h}$$

Journey time, journey speed and running speed

Mean stopped delay: N-S 1.342 min, S-N 1.458 min.

$$\begin{aligned} \bar t_{NS} &= t_w - \frac{y}{q} = 4.381 - \frac{1.00}{4.21} = 4.143\ \text{min}, & \bar t_{SN} &= 4.336 - \frac{0.83}{4.34} = 4.144\ \text{min}\\ V_j &= \frac{L}{\bar t}: & V_{j,NS} &= 369.3\ \text{km/h},\ V_{j,SN} = 369.2\ \text{km/h}\\ V_r &= \frac{L}{\bar t - \text{delay}}: & V_{r,NS} &= 546.2\ \text{km/h},\ V_{r,SN} = 569.7\ \text{km/h} \end{aligned}$$

Answer:

Note: a section of 25.5 km run in about 4.4 minutes implies unrealistic speeds, so the length is probably 2.55 km. Flows are unaffected; the speeds would then be one-tenth of those above (36.9 and 36.9 km/h journey speed, 54.6 and 57.0 km/h running speed).