HS 125 Series
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Flight Engineer
Flight Crew Total 20250; Flight Crew Type 550
Confusion
Aircraft Equipment Problem Critical; Deviation - Altitude Undershoot; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Returned To Departure Airport; Flight Crew Took Evasive Action; General Maintenance Action
Aircraft
[After] boarding the passengers; we started our taxi. As we were cleared for takeoff on the rolling out; the airspeed was alive reaching 80 knots. V1 and VR all the instruments were working perfect. Leaving the ground and climbing at 400 feet; yaw damper was unable to engage. The ZZZ Tower transferred us to departure frequency by reaching 1;500 feet. At 1;500 feet.; the auto-pilot was unable to engage and received instruction from ATC to turn heading 210 degrees and climb to 6;000 feet. At that moment; the airspeed indicator on the Captain side was gone and since the copilot side was showing the airspeed indication; the controls [were] transferred. As we reached 6;000 ft. and leveled; ATC called us asking if we were climbing and we responded negative we are level off at 6000 ft. ATC said negative you are at 2;500 feet. We noticed that the R/H side altimeter and Standby Altimeter were showing an altitude that we were not at. We request to return to ZZZ due to instrument failure; by then; ATC recleared us to descend to 4;000 feet. and heading 270; with the RH ADI showing a pitch of 15 nose down and climbing; so flight controls was transfer again to Captain. The altimeter at the Captain side was showing the more[or] less [than] the altitude from ATC. They gave us radar vectors for the ILS RWY XX and ZZZ circle to land to RWY XY. We told the ATC to give us vector to final Runway XX and that we were to land in that runway; due since we couldn't rely on the instruments; neither the ILS. When we landed there were fire-rescue trucks and an ambulance. ATC asked us if we needed any assistance and we said no; so we taxi.
HS125 Captain reported erroneous airspeed and altitude indications led to a return to the departure airport.