## 1 Introduction  
When the carrier-based aircraft takes off with catapult assist, the holdback bar is connected to the torque arm joint of the nose landing gear and the holdback bar device on the deck, respectively, and the launch bar on the nose landing gear is connected to the catapult shuttle on the deck. Under the combined effect of the catapult and engine thrust on the aircraft, the holdback bar is tensioned, and when the force applying on the holdback bar reaches the release load, the bar is quickly discharged from the nose landing gear, so that the aircraft is released from the restraint of the holdback bar and starts gliding. To reach the safe takeoff speed of the carrier-based aircraft within the limited gliding distance, ensuring the magnitude and accuracy of the holdback bar release load is necessary. One-time holdback bars were used in the 1960s, and research on repeatable holdback bars began in the United States in the 1970s [1]. The literature [2; 3; 4] gives the design requirements for the nose landing gear before catapult-assisted takeoff of the carrier-based aircraft, as well as for the holdback bar, which needs to be accurately controlled within 0-6% of the release load in a certain temperature range. As catapult-assisted takeoff method was adopted for carrier-based aircraft, scholars around the world have conducted many in-depth studies on the catapult-assisted takeoff process: In [5], the catapult performance of several aircrafts were analyzed and the criteria for the catapult-assisted takeoff based on the departure speed was given out. In [6], dynamics analysis and calculations were carried out for the catapult-assisted takeoff process and the landing block process; in [7; 8; 9], the parameters affecting the catapult-assisted takeoff were analyzed, and the influence of the sudden extension of nose landing gear on the catapult process was studied; in [10], the minimum departure speed of F/A-18E/F during catapult-assisted takeoff was studied; in [11], a multi-agent based carrier-based aircraft catapult-assisted takeoff model under the effect of wind field environment was established; the paper in [12] investigated the rapid vibration phenomenon of the nose landing gear along the heading direction when the holdback load was suddenly unloaded and analyzed the loading condition of the nose landing gear. The work in [13] studied the impact of the launch bar's restoring moment and weight on the dynamic performance of the launch bar itself; the work in [14] established a catapult dynamics model including the mass of catapult shuttle and analyzed the dynamic response of the towing process after the discharge of the holdback bar till the discharge of the launch bar; the works in [15; 16] studied the dynamic change law during the catapult-assisted takeoff, and the influence of the acceleration and flight trajectory under different parameters on the catapult safety of the carrier-based aircraft; the work in [17] studied the influence of the carrier in different initial phase of vertical toss on the sinking of the carrier-based aircraft during the catapult-assisted takeoff process; the works in [18; 19] analyzed the suitability of F-35 on aircraft carriers, as well as the catapult-assisted takeoff and blocking tests on aircraft carriers. The work in [20] investigated the effect of deck motion on the catapult takeoff characteristics of a carrier-based aircraft. In [21], an experimental study was conducted on the sudden extension performance of the nose landing gear of a naval aircraft. In [22], a variable topology solution method with real-time adjustment during the catapult takeoff of the carrier-based aircraft was studied. In [23], the effects of surface rocking of the aircraft carrier and side wind on the catapult takeoff of aircraft were investigated. The catapult-assisted takeoff of a carrier-based aircraft mainly consists of three phases: the tensioning phase, the catapult gliding phase, and the departure phase.