Date: 202201
Local time of day: 1801-2400
Location: ZZZ.Airport, US
Flight conditions: IMC
Weather elements / visibility: Fog; Icing
Light: Night
Aircraft: B747-400
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Cargo / Freight / Delivery
Flight phase: Taxi
ATC / advisory: Ramp ZZZ
Aircraft component: Engine Starting System
Component problem: Malfunctioning
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Flying
Reporter qualification: Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Human factors: Human-Machine Interface; Communication Breakdown; Situational Awareness
Second reporter function: First Officer; Pilot Not Flying
Anomaly: Aircraft Equipment Problem Less Severe; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Ground Equipment Issue; Ground Event / Encounter Vehicle; Ground Event / Encounter Loss Of Aircraft Control
Detector: Person Ground Personnel
When detected: Taxi
Result: Air Traffic Control Provided Assistance; Aircraft Aircraft Damaged; Flight Crew Requested ATC Assistance / Clarification; Flight Crew Returned To Gate; General Flight Cancelled / Delayed; General Maintenance Action
Contributing factors: Aircraft; Human Factors; Procedure
Primary problem: Procedure

Narrative: It was night with freezing fog and visibility in the low RVRs. After de-icing / anti-icing and checklists complete; I was in contact with the ground crew at parking spot XX. He had me release the brakes to move the airplane; straighten the nose and remove chocks. We felt the airplane move backward and jerk heavily side to side. We were under tow. Ground crew cleared us to start all engines. I confirmed starting engines 4 and 1; he confirmed it is clear. After these started; I confirmed starting engines 2 and 3; and he confirmed it is clear. Engine 3 failed to start. I called for the immediate action items for the EICAS message ENG 3 AUTO START; and immediately after that for the QRH. While the FO (First Officer) was reading the QRH the ground crew interrupted and said we had 4 good engine starts. I immediately responded Negative; engine 3 did not start. I repeated it a few times but no answer. Now we saw the airplane start to move forward slowly. I urgently called the ground crew again because I did not want to step on the brakes while we were under tow and cause extensive damage. There was no answer so I brought the airplane to a stop on taxiway 1 in front of our parking spot. I continued calling the ground crew and flashed the lights to signal the ground crew; and they gave us hand signals to turn off the engines. After connecting to the interphone; the ground crew informed us that a cart bounced the exhaust cone of engine 3. After we pushed back to the parking spot and exited the airplane we saw the scrape on the engine 3 tail cone. In conclusion; we all thought we were under tow because the airplane was moved to remove chocks and straighten the nose wheel; and the slope is also slightly downhill.  The ground crew did not say to set the parking brake; he just cleared us to start engines; so we rightfully thought we were still connected to the tug. The ramp was icy and another 747 had to be towed into a spot in front of us after sliding on the ramp. I was dealing with the engine malfunction and emergency checklist and calling the ground crew when we saw the airplane move and brought it to a stop. A lot was happening at the same time and it can occupy one's attention. Everything was giving us the assurance that we were under tow. Clear instructions need be communicated to the flight crew if towing will be used or not be used; especially in situations of inclement weather; poor visibility and at night. I suggest that when cleared to start engines; the crew always be directed to set the parking brake. It is imperative that ALL objects in front of the engines; wings and airplane be removed before starting engines; not after. This would have prevented this mishap.


Second narrative: While parked on XX; communication was established with the ground crew. They asked the Captain to release the parking brake in order to straighten the nose wheel.  The Captain requested confirmation that they would like him to release the brake to which they confirmed.  A moment later the plane jostled; consistent with a tug gaining control of the aircraft.  All required checklists were completed. ZZZ ground was called to obtain clearance for engine start and they approved. This was communicated to the ground crew and they responded that we were cleared to start all engines. Engines 4 and 1 started normally at which time the ground crew cleared us to start engines 2 and 3.  Engine 2 started normally and we even made note at how engine 3 was taking longer than normal.  At that time an ENGINE 3 AUTO START EICAS message appeared.  The Captain appropriately called for the immediate action items and the First Officer promptly ran the checklist.  Once that checklist was complete the Captain called for the QRH procedure.  Shortly into that checklist; the ground crew called and said; 'it appears you have 4 good engine starts are we cleared to disconnect.' The Captain immediately responded; 'negative; no engine start on 3.' Without getting a response from the ground crew; the FO continued with the QRH checklist at which time we noticed the plane starting to move.  Again the Captain called the ground crew to inform them to stop and that we did not have 4 good engine starts.  We rolled what appeared to be 20 feet when after multiple calls to the ground and an aircraft ahead of us; we realized that no one was connected to the headset below or at a minimum were not responding to us.  The Captain used the toe brakes to bring the plane to a stop.  Once stopped he attempted to contact the ground crew again.  Having three engines running; and the immediate action items complete for the third engine; and partially done with the QRH procedure the FO continued with the checklist.  While we were running that checklist we got the hand signals from the ground crew to shutdown the remaining engines.  All engines were shut down upon that request. While there are a number of things that could have been done better in this situation; the only thing that would have prevented aircraft damage regardless of all other factors would have been if all equipment had been removed from the safety area before we were given the clearance to start engines.  I will not claim to know the procedures of the ground crew but based on their actions it seems as though their standard procedure is to leave a cart or small vehicle in front of the plane regardless of whether they are using it for aircraft push back.  As a result in this incident; it was that small vehicle that was struck by the plane causing the damage.  I would suggest that if a tug is not being used for push back that ALL vehicles must be removed to the safety area before a clearance has been given to start engines


Synopsis: B747-400 flight crew reported a malfunction during engine start was not observed by the ground crew during push back. The ground crew disconnected the tug without asking the Captain to set the parking brake. The aircraft rolled into a parked cart and damaged an engine inlet.