Effects of booms of a sounding rocket on rocket charging and on the local plasma conditions are studied with numerical and analytical models accounting for flowing, ionospheric plasmas. Simulations are carried out with a first principles self-consistent Particle-In-Cell numerical code. It is shown that the booms can affect the charging of the payload and disturb the local plasma to a high degree. The boom-to-plasma potential, which varies with the position due to the convective electric field, can lead to significantly different currents, in particular electron currents, to the booms on either side of the rocket. The analytical models for the collected currents considered in this study show good agreement with the simulations. The potential difference between the plasma and the rocket can electrostatically focus the ions to create regions of enhanced ion density downstream of the rocket and can lead to an asymmetric wake. It is shown that ion focusing can be asymmetric between the booms due to the potential gradient. These effects can have implications for instrument placements and data analysis.