Development and damping characterisation of an ice climbing tool with rubber-interleaved carbon-aramid shaft

Abstract

Every strike with an ice tool transmits impulsive shock and vibration to the climber’s hand-arm system while ascending – leading to discomfort. The developed prototype ice tool features a fibre-reinforced polymer shaft with an interleaved viscoelastic layer in a carbon-aramid hybrid laminate, aiming to enhance climbing efficiency through increased damping. By vacuum split moulding the shaft, a 43% weight reduction over aluminium at 50% fibre volume fraction is achieved. The prototype’s damping ratio was then compared with three conventional ice tools. An accelerometer on the back of the hand measured the hand-arm vibration response during and after impact, while a force plate standardised the peak contact force. Lighter ice tools must be accelerated more to achieve the same impact energy. Results indicate that this requirement leads to higher vibration exposure of the hand-arm system. Incorporating rubber foil improved vibration damping and potentially impact attenuation, though performance differences were limited due to the system’s overall high stiffness.

Keywords

vibration damping interleaved viscoelastic layers carbon-aramid hybrid laminates fibre-reinforced polymer composites hand-arm vibration impact attenuation sports equipment dynamics

Introduction

Ice climbing is a form of mountaineering where climbers ascend vertical terrains (such as ice falls) in a quadrupedal manner, using technical ice axes (ice tools) in each hand and crampons on each foot. It has developed as an extreme sport ranging from “pure” ice climbing to dry tooling, including rock sections in parts of the route and as a regulated competitive sport that includes artificial structures. UIIA World Cup Championships began in 2002 and the sport’s rapid growth has led to ice climbing being showcased as a demonstration sport at the Winter Olympics in Sochi in 2014.

Each placement of an ice tool must be accurate and forceful enough to “bite” securely into the ice, supporting the climber’s weight. Often, multiple swings are required to set a reliable anchor in hard ice, demanding a balance of strength and precision in every strike.¹ In the last few decades, the design of ice tools had to evolve to meet these advanced functional requirements. While seeking a lightweight design, high stiffness, strength and optimal weight distribution, materials to manufacture an ice tool varied from aluminium and magnesium to carbon and aramid fibres.² Modern ice axes have short, ergonomically curved shafts and aggressively angled picks (typically 60° pick-to-shaft angle) to improve swing efficiency and placement security.¹ The most conventional ice tools are made of aluminium. Further developed models combine aluminium with fibre-reinforced composites or are made entirely of composites – such as the hand-made Morpho from EliteClimb.

However, each strike transmits impulsive shock and vibration through the tool into the climber’s hand, wrist and arm, leading to discomfort. Rouard et al.¹ revealed in their biomechanical study on ice tool swinging movement that the muscles responsible for gripping the ice tool, particularly the flexor digitorum muscles, experience high activation and fatigue. Additionally, immediately prior to impact, a strong co-activation of upper limb muscles occurs to maximise force transmission and control.¹ This coordinated stiffening of shoulder, arm and forearm muscles at impact stabilises the joints and maximises force transmission into the ice.¹ The intense grip ensures that the impact energy is effectively transferred to the ice for a solid placement. As a result, the climber’s hand-arm system directly experiences the impulsive shock from the strike. Over repeated swings, this dynamic places substantial strain on the wrist and the forearm. ISO 5349-2 evaluates human exposure to hand-transmitted vibration using handheld machines and tools. It states, “vibration exposure can also be associated with a reduction in grip strength”³. Furthermore, ISO 28927-10:2011, specifying methods for measuring hand-arm vibration in power-driven percussive machines, states, “impulsive shocks can significantly impact the hand-arm system, leading to discomfort and potential reduction in grip strength”⁴. Although ice climbers are not subjected to continuous vibration as individuals using tools, these standards underline the discomfort experienced by ice climbers and suggest that impulsive shocks and resulting vibration can negatively affect the grip force. Round et al.¹ demonstrated that grip strength fatigues more rapidly while ice climbing than other muscle groups.

This research develops a concept for an ice tool with increased damping capabilities to enhance climbing efficiency and mitigate the described adverse effects. It presents a novel hybrid composite design for ice axe shafts, combining carbon and aramid fibres with an embedded rubber foil layer to dampen vibration and reduce weight.

Interleaved rubber foils are typically used to improve dynamic response due to their damping effect, for example, in alpine ski applications.⁵ These viscoelastic inclusions dissipate vibration energy through shear deformation during flexion, thereby converting it into heat. Research in composite materials confirms that various interleaves with viscoelastic properties, like ionomers, thermoplastic-elastomer films and rubber nanofibres, can significantly improve damping properties in fibre laminates.^6–8 An additional advantage is gained through enhanced fracture toughness compared to non-interleaved composites, essential for ice tools subjected to high abrasive wear.^6,8 However, these benefits come with a trade-off, as adding interleaves can reduce stiffness and strength. For example, Akimoto et al.⁸ noted a decrease in flexural modulus with softer interlayers, illustrating the challenge of balancing damping and mechanical performance.

Our study aims to fill a significant gap in climbing research by scientifically examining a vibration-damping ice axe shaft, potentially contributing new insights into composite engineering that enhances user experience and performance in ice climbing as an extreme sport. Given this context, this study addresses a novel interdisciplinary research question: Does integrating a rubber foil interleaf into a composite fibre-reinforced ice axe shaft reduce the vibration transmitted to an ice climber’s hand-arm system?

Materials and Methods

Product design of the prototype

Manufacturing concept

Three concepts for the potential production of the composite ice tool shaft were evaluated. Filament winding, the autoclave process using prepreg and the hand lay-up with vacuum pressing. The vacuum pressing process involves manually impregnating the fibres with resin, followed by pressing at a maximum of 1 bar ambient pressure. The fibre volume fraction is generally at 40% to 50%.⁹ Despite a relatively lower fibre volume fraction, this processing method achieves high strengths.⁹ Additionally, the associated investment costs are minimal. Consequently, the decision was made in favour of vacuum pressing.

Geometry

The prototype was manufactured with the exact geometry of the test object X-Dream to exclude geometric influences on the vibrational behaviour when comparing these two ice tools. C.A.M.P. SpA provided the handle, pick and two mounting inserts shown in Figure 1.

Figure 1.

Ice tool prototype.

Laminate layup

To increase the fracture toughness and abrasion resistance of the composite shaft – which are the most significant disadvantage compared to a ductile material such as aluminium – the carbon/aramid twill “HP-T205AC”¹⁰ with a $+ 45^{°} / - 45^{°}$ fibre orientation along the shaft axis (Figure 1) was used for the outermost layer because aramid fibres have excellent abrasion resistance properties. Perforated “Semperit Anti-Torsion Foil”⁵ was selected as the second layer to increase impact resistance further. The holes in the rubber foil increase the torsional rigidity and allow excess resin to drain off during vacuum pressing (Table 1).

Table 1.

Laminate stacking sequence (thicknesses calculated for a fibre volume fraction of 45%).^5,10,11

Layer	Fibre material	Areal mass ( $g / m^{2}$ )	Orientation (°)	Thickness ( $mm$ )
1	Carbon/aramid	205	+45/−45	0.26
2	Rubber foil	210	–	0.20
3	HT Carbon 50K	300	+45/−45/0	0.38
4	HT Carbon 50K	300	+45/−45/0	0.38
5	HT Carbon 50K	300	+45/−45/0	0.38
6	HT Carbon 50K	300	+45/−45/0	0.38
7	HT Carbon 50K	300	+45/−45/0	0.38

Layers three to seven consist of the triaxial carbon fibre fabric “HP-T300C”¹¹ and are the ice tool’s load-bearing structure. Each triaxial layer consists of three plies, resulting in five carbon layers with a total of fifteen plies. The $+ 45^{°} / - 45^{°} / 0^{°}$ fibre arrangement forms a balanced layup that increases rigidity and reduces interlaminar shear between adjacent plies with differing orientations. Owing to this balanced layup, the laminate was simplified as quasi-isotropic for the subsequent strength estimation. While the fibres in the $0^{°}$ -direction along the pick shaft bear most of the bending-induced axial normal stresses (tension and compression), the $\pm 45^{°}$ -oriented fibres ensure torsional rigidity.

A fibre volume fraction of 45% is assumed, leading to an estimated wall thickness of $2.36 mm$ . Under load, the rubber-foil interleaf experiences only negligible stress; thus, interlaminar stress transfer between layers three and one is low. For strength verification, only the five carbon layers were considered load-bearing, and the two protective layers were omitted.

Strength verification of the carbon core

The strength requirements of an ice axe are defined by the test methods of the DIN EN 13089 standard.¹² Ice axe models are divided into two categories:

Type 1 (category B – basic): Ice axe with straight shaft for use in snow and ice.

Type 2 (category T – technical): Ice axe with curved shaft for use on rock, snow and ice (significantly higher strength requirements).

Our prototype must fulfil the “technical” requirements. Maximum stresses occur during the strength test “5.3.5 Strength in load direction XX,”¹² as the shaft can sustain a lower bending moment in the XX direction than in the YY direction due to its oval geometry. The ice tool is loaded with $4000 N$ at the head and supported by a tape loop and a rounded stop, as shown in Figure 2, such that the ice-tool pick lies perpendicular to the direction of the applied force.¹²

A maximum bending moment was calculated using static mechanics. Due to the shaft’s curvature, the applied loading induces coupled bending-torsion; however, the torsional moment T was omitted for simplicity. The maximum bending moment $M_{B, XX} = 468.75 Nm$ was determined as displayed in Figure 2, assuming a uniformly distributed line load transferred by the tape loop.

The quasi-isotropic carbon layup allowed the bending strength to be estimated using the Euler–Bernoulli beam theory.¹³

The $1.9 mm$ thick carbon core has a second moment of area of $I_{yy} = 5323 {mm}^{4}$ . Using the maximum edge distance $x_{\max} = 8.8 mm$ of the outermost fibre to the neutral axis, shown in Figure 3, the section modulus about the y-axis (YY) was obtained:

W_{y} = \frac{I_{yy}}{x_{\max}} = 604.89 {mm}^{3}

(1)

A permissible flexural strength was calculated using the Rule of Mixtures.¹⁴ The fibre volume fraction $V_{f} = 0.45$ , a typical tensile strength of HT (high tensile strength) fibres $R_{m, f} = 4000 N / {mm}^{2}$ ¹⁵ and the matrix flexural strength of the epoxy resin system “L+LT”¹⁶ $σ_{B, m} = 156 N / {mm}^{2}$ ¹⁷ were taken into account. In the special case of the triaxial fabric, one-third with $0^{°}$ -oriented fibres carries most of the bending-induced axial normal stresses. The two-thirds with ± $45^{°}$ fibre orientation were considered with the factor $\cos^{2} (45^{°}) = 0.5$ according to the stress transformation formula of laminate theory:¹⁴

σ_{B, f, 0} = R_{m, f}

(2)

σ_{B, f, 45} = R_{m, f} \cdot 0.5

(3)

Tensile strength values overestimate the effective flexural strength of ± 45°-oriented fibres under bending deformation. Thus, the total flexural strength was multiplied by a reduction factor of 0.7.^18,19 This empirical factor accounts for the simultaneous occurrence of tensile, shear and compressive stresses during bending, whereby the compressive strength of fibre-reinforced composites is typically lower than the tensile strength.^18,19 The formula for flexural strength is:

\begin{matrix} σ_{B} = (\frac{1}{3} \cdot V_{f} \cdot σ_{B, f, 0} + \frac{2}{3} \cdot V_{f} \cdot σ_{B, f, 45} + (1 - V_{f}) \cdot σ_{B, m}) \\ \cdot 0.7 = 900.06 N / {mm}^{2} \end{matrix}

(4)

This results in an estimate of the maximum permissible bending moment:

\begin{matrix} M_{B, \max} = W_{y} \cdot σ_{B} = 544.44 Nm \\ \Rightarrow M_{B, \max} = 544.44 Nm \geq 468.75 Nm = M_{B, XX} \end{matrix}

(5)

The bending moment in the XX direction is lower than the maximum permissible bending moment. These calculations confirm that five layers of $300 g / m^{2}$ triaxial carbon fibre fabric are suitable for manufacturing an ice tool prototype.

Figure 2.

Strength test setup in load direction XX according to DIN EN 13089.¹² Graphical representation of the results from static mechanical calculations (Dimensions in mm).

Figure 3.

Shaft profile: laminate layer overview.

Manufacturing and assembly

The split mould shown in Figure 4 was used to produce the ice tool shaft. The two split moulds correspond to the negative of one-half of the shaft. The PLA mould halves were mounted on wooden support plates and perforated to allow excess resin to escape. At the beginning of the lamination process, the resin and the hardener were mixed with a 90-min processing time before curing.¹⁶ The layers were placed in the respective mould half, fixed in place with spray adhesive and manually impregnated with resin, starting with the outermost layer. The ten carbon half-layers were cut to fit, overlapping to prevent weak points at the contact point of the mould halves. After 14 half-layers had been positioned, the vacuum tube was placed between the upper and lower moulds. The mould halves were folded, aligned and centred using two centring cone inserts with counter bushes. Protective adaptors prevented sharp edges from damaging the vacuum tube. Bleeder fabric wrapped around the mould absorbed excess resin. The assembly was sealed in a vacuum bag and air was removed to create a $0.89 bar$ vacuum. The ambient pressure caused the vacuum tube inside the mould to expand and pressed the fibre layers from the inside out.

Figure 4.

Exploded view of the split mould used for vacuum pressing.

After curing for 24 h under pressure, we separated the moulds using wedges and removed the shaft. A heat treatment was performed for 16 h at 70°C, with heating and cooling gradients of 10°C/h, to improve the cross-linking and reduce brittleness.¹⁶ The trimmed shaft weighed $102 g$ and had a fibre volume fraction of 50%. Overlapping layers led to an uneven wall thickness, requiring material removal with a Dremel to fit the aluminium mounting inserts for the handle and pick. These inserts were bonded with epoxy resin and secured using two countersunk screws and two countersunk sleeve nuts each. A surface coating to protect the aramid fibres from UV-induced material degradation was omitted for the prototype. Finally, the pick and handle were fastened using one M8 screw and nut for each part.

Ice tool strike test: Measuring hand-arm vibration response

The prototype and three further ice tools were tested to determine the influence of the interleaved rubber foil layer on the damping properties. Test objects:

(i) X-Dream produced by C.A.M.P. SpA

(ii) Prototype

(iii) Morpho produced by EliteClimb

(iv) Ergonomic produced by Petzl

Measurement placement

The accelerometer’s positioning significantly affects measurement accuracy and comparability across test setups. Three configurations were evaluated: (1) affixed to the shaft above the handle, (2) mounted on the handle and (3) positioned on the back of the hand.

Mounting on the shaft ensures maximum measurement accuracy due to minimal relative motion between the sensor and test object but neglects the transmission through the handle to the hand-arm system. Placement on the handle, while standard for vibration emission measurements,^3,4,20 was excluded as it interferes with regular ice tool usage because the handles of the ice tools only offer space for the hand. The final configuration placed the sensor on the back of the hand, allowing a realistic representation of the climber’s vibration exposure despite the damping effects of the hand. The independence of varying shaft geometries, which occur as interfering variables, enables consistent comparison of the measurement results.

Testing setup

A “StickC-Plus2”²¹ accelerometer was used with a range of $\pm 16 g$ and a sampling rate of $500 Hz$ . This low-cost, cable-free device was selected for its practicality and using the identical sensor-mounting setup in all tests ensured that any bias affected all ice tools equally. The sensor ( $48.0 \times 24.0 \times$ 13.5 mm) was mounted on a PLA holder with a concave base and fixed using elastic cords around the index finger, little finger and wrist. Additionally, a thin skin-adhesive layer was applied to prevent relative movement of the sensor-mounting setup; owing to its minimal thickness, its effect on vibration transmission was considered negligible for the purposes of between-tool comparison. The coordinate system alignment is shown in Figure 5.

Figure 5.

Schematic testing setup.

Force measurements were recorded using a Kistler force plate “9286B”²² mounted at a $20^{°}$ tilt on an aluminium profile support structure fixed to a table. The setup required a seated position but offered sufficient isolation from structural vibration. The force plate, designed for 3D force measurement, was covered with a $27 mm$ thick wood protection. The impact blocks ( $100 \times 100 \times$ 70 mm) were inserted through a cut-out in the wood protection in direct contact with the aluminium surface of the force plate. The ice blocks used in the tests must be clamped to prevent splintering. Therefore, three wooden profiles were screwed onto the wood protection. Clamping is then performed in the positive y-direction of the force plate (see Figure 5) using a fourth wooden profile, secured by two vertical screws and in the z-direction with TPU fixtures, which press the test blocks onto the force plate.

Test procedure

The test object type served as the independent variable; measured acceleration amplitudes at the back of the hand were the dependent variable. Impact surface and force were standardised. The subject (height: $185 cm$ ) was seated upright on the floor. The impact block centre was positioned $65 cm$ in front of and $125 cm$ above the sitting position. Strikes to the impact block were delivered with the right hand in a controlled manner, while not wearing gloves. For all tools, the climber used the lower primary grip position with the base of the palm on the support horn and kept a firm, consistent grip across strikes. Measuring grip force during the strikes was not implemented, as additional sensors at the handle would have altered the natural vibration transmission.

Test series 1: Polycarbonate

Four test objects (i–iv) were examined. The accelerometer remained fixed throughout the test series. The impact block consisted of a $62 mm$ thick birch wood base with an $8 mm$ polycarbonate sheet mounted on top. The pick rebounded upon impact. Each test object was used for 160 impacts, divided into four sets of 40 strikes. The test objects were rotated after each set to minimise confounding variables, especially fatigue-related grip force changes. The polycarbonate sheet was replaced after each set to ensure consistent surface conditions. Five-minute rest intervals were included between sets to minimise fatigue-related changes in grip force.

Test series 2: Ice

This series involved test objects X-Dream (i) and prototype (ii). The impact surface consisted of firmly clamped $70 mm$ thick ice blocks to simulate realistic conditions. Ice blocks were removed from a freezer at $- 12^{°} C$ shortly before use. For each test object, 34 valid impacts were recorded. A total of 40 ice blocks were used. Exclusively impacts on undamaged ice surfaces were considered valid, with blocks being replaced after one to three hits. Only isolated strikes remained anchored; most rebounded despite initial penetration due to the brittle-fracture behaviour (chipping/spalling) of the ice around the pick.

Data processing

Selection of minimal peak contact force range

The z-axis force component (perpendicular to the force plate) was used to ensure consistent loading conditions across test objects; the exact pick-to-surface impact angles were not quantified. The force plate’s 1000 Hz sampling rate was insufficient to capture the true peak contact force. Therefore, to enhance the comparability, each peak was approximated by the mean of the peak value and its closest neighbour within a time window of $\pm 1 m s$ . In rare impact events where the force signal exhibited two closely spaced local maxima within a single strike (double impact likely due to variations in ice properties), the peak contact force was defined as the higher of the two maxima before applying this averaging procedure. A MATLAB programme sorted impact data and iteratively selected the minimal range that met the required sample size. The programme dynamically adjusted the range by expanding it when necessary, ensuring that each test object contributed the required number of values. In test series 1 (n=25), 100 of 640 total impacts (four test objects) were selected within a $199 N$ range (2132–2332 N). For test series 2 (n=15), 30 of 68 total impacts were selected within 800–950 N.

Filtering

Accelerometer data from the selected strikes, nominally sampled at $500 Hz$ (actual mean $492.07 Hz$ , SD $0.13 Hz$ , n=100), was linearly interpolated to $1000 Hz$ . Impact data were offset-corrected by adding the estimated gravity component (6.936 m/ $s^{- 2}$ ) based on the sensor impact orientation. For each impact, the mean of the absolute values of the unfiltered resampled acceleration signal was computed as the vibration measure (see Tables 3 and 4).

A third-order Butterworth band-pass filter (0.5–100 Hz) was applied using MATLAB’s butter and filtfilt functions to eliminate noise without phase shifts. This filtering enabled accurate peak amplitude detection in the following processing step.

Vibration analysis via curve fitting

Positive acceleration peaks were identified using prominence, distance and height thresholds. Then an exponential decay function $A = A_{0} \cdot \exp (- λ \cdot t)$ was fitted using lsqcurvefit, where A₀ represents the starting amplitude and λ the damping factor. The damping ratio ζ was determined from the damping factor λ and the damped natural frequency f_d according to:

ζ = \frac{λ}{2 π f_{d}} = \frac{λ}{ω_{d}}

(6)

(ω_d is the damped natural angular frequency). This approach allowed for the comparison of damping characteristics across test objects.

Results

The impact impulse generated by an ice tool strike is transmitted from the impact surface into the pick and then transferred to the hand-arm system. The accelerometer y-axis, shown in Figure 5, was nearly parallel to the ice tool picks when hitting the impact surface. Thus, the y-direction accelerometer data is used to evaluate the vibration exposure on the participant’s hand-arm system.

Two time periods were considered. Firstly, $350 ms$ during the striking phase of the ice axe moving towards the target. Secondly, $150 ms$ which include the impact and rebound of the ice axe. This time range (see Figure 6) contains the highest acceleration amplitude and is relevant for assessing the vibration exposure of the hand-arm system.

Figure 6.

Filtered acceleration data plot of 25 X-Dream impacts on polycarbonate (moment of impact $\approx 40 m s$ ).

Test series 1 results: Polycarbonate

During the striking phase, the y-axis of the accelerometer points against the direction of movement of the hand, which hurls the ice axe forward in a throwing-like motion.¹ Therefore, the measured acceleration values are negative during motion towards the target.

The mean values of the acceleration data during the striking phase (Table 2) showed that the two lighter composite materials, ice tools (ii) and (iii), were each accelerated significantly more than the heavy aluminium ice tools. There was no significant difference between X-Dream (i) and Ergonomic (iv) (p=0.801), nor between prototype (ii) and Morpho (iii) (p=0.613).

Table 2.

Unfiltered acceleration mean values during the striking phase of the four test objects over $350 ms$ (without gravity offset-correction).

No.	Icetool	Mass ( $g$ )	Mean ( $m / s^{2}$ )	SD ( $m / s^{2}$ )
(i)	X-Dream	595	−10.046	1.149
(ii)	Prototype	518	−11.863	1.104
(iii)	Morpho	390	−11.503	0.800
(iv)	Ergonomic	645	−9.780	1.071

The mean absolute acceleration data from Table 3, measured on impact with polycarbonates, shows that the composite ice axes prototype (ii) and Morpho (iii) each generate a significantly higher vibration exposure at the same peak contact force range than the two aluminium shaft ice tools X-Dream (i) and Ergonomic (iv). No significant difference was found between X-Dream (i) and Ergonomic (iv) (p=0.970).

Table 3.

Unfiltered acceleration mean values over 150 ms (n= 25, peak contact force range: 2132–2332 N).

No.	Icetool	Shaft material	Mean ( $m / s^{2}$ )	SD ( $m / s^{2}$ )
(i)	X-Dream	Aluminium	28.610	1.229
(ii)	Prototype	Carbon/aramid/rubber	32.318	2.252
(iii)	Morpho	Carbon/aramid	30.696	1.703
(iv)	Ergonomic	Aluminium	28.367	1.972

The filtered acceleration curves in Figures 6 and 7 illustrate the acceleration profiles during impact and rebound. The prototype exhibits a higher peak acceleration of approximately 155 m/s⁻², compared to the aluminium X-Dream, which reached approximately 100 m/s⁻².

Figure 7.

Filtered acceleration data plot of 25 prototype impacts on polycarbonate (moment of impact $\approx 40 m s$ ).

Furthermore, Figures 6 and 7 show that vibration amplitudes decay faster with the prototype than with the X-Dream, a trend made clearer by the addition of qualitative exponential decay curves. This trend is also evident in the vibration analysis results displayed in the box plot 8. The damping ratio ζ was calculated for each impact from the fitted exponential decay. Figure 8 shows the distribution of damping ratios for the four test objects. The prototype exhibits the highest mean damping ratio (ζ= 0.1138), followed by Ergonomic (ζ= 0.1056), Morpho (ζ= 0.1020) and X-Dream (ζ= 0.0777).

Figure 8.

Test series 1: Calculated damping ratios (n= 25, peak contact force range: 2132–2332 N).

Post-hoc Tukey–Kramer tests revealed that the X-Dream differs significantly from all other tools (all $p < 10^{- 6}$ ). The prototype shows significantly higher damping than the Morpho (p=0.047); however, the differences between prototype and Ergonomic (p=0.238) and between Morpho and Ergonomic (p=0.849) were not statistically significant.

Test series 2 results: Ice

Acceleration responses on ice were overall higher (Table 4). The comparison of the vibration analysis results for the X-Dream and the prototype did not reach statistical significance (p=0.243). Detecting the between-tool damping differences requires a larger number of impacts and tighter standardisation of strike conditions. As a methodological outcome, this test series establishes an on-ice protocol for future between-tool comparisons under realistic conditions.

Table 4.

Unfiltered acceleration mean values over 150 ms upon impact on ice blocks (n= 15, peak contact force range: 800–950 N).

No.	Icetool	Mean ( $m / s^{2}$ )	SD ( $m / s^{2}$ )
(i)	X-Dream	38.53	4.228
(ii)	Prototype	36.631	4.489

Discussion

The mean acceleration values from Table 3 indicate that the two composite ice tools, prototype (ii) and Morpho (iii), cause a higher overall vibration exposure than the two aluminium ice tools, X-Dream (i) and Ergonomic (iv). The higher vibration exposure correlates with the increased accelerations during the striking phase observed in Table 2. These findings confirm that the lightweight composite ice tools (ii and iii) require a higher impact velocity to generate the same peak contact force as the aluminium ice tools (i and iv).

Damped harmonic oscillator model

To explain why the enhanced damping properties of the prototype did not reduce the overall vibration exposure compared to the other test objects, we consider a damped harmonic oscillator model. The equation of motion is given by:

m \overset{\cdot\cdot}{x} (t) + c \overset{\cdot}{x} (t) + k x (t) = F (t)

(7)

We assume an impulsive excitation $F (t) = F_{0} δ (t)$ that instantaneously imparts an initial velocity. The system is underdamped with a damping ratio ζ < 1 and follows a free oscillatory response. The displacement is described by:

x (t) = A e^{- ζ ω_{n} t} \sin (ω_{d} t)

(8)

where $ω_{n} = \sqrt{k / m}$ is the undamped natural frequency, $ω_{d} = ω_{n} \sqrt{1 - ζ^{2}}$ is the damped natural frequency and $ζ = c / (2 \sqrt{km})$ is the damping ratio. The amplitude A is proportional to the initial velocity imparted by the impulse $A \propto \frac{F_{0}}{m ω_{d}}$ . The maximum acceleration can be estimated by differentiating x(t) twice and evaluating near the first peak, where $\sin (ω_{d} t) \approx 1$ . Resulting in the approximation:

a_{\max} (t) \propto \frac{F_{0} \sqrt{k}}{m^{3 / 2}} e^{- ζ ω_{n} t}

(9)

This formula summarises the dynamic response of an ice tool, where F₀ is the peak contact force, k is the spring constant and $ζ ω_{n} = λ$ represents the damping factor. It highlights how the peak contact force and the engineering-controllable parameters – stiffness, mass and damping coefficient – influence the maximum acceleration and, thus, the vibration exposure after the impact.

The formula (9) is now applied to compare the effects of the engineering parameters of the prototype and the X-Dream at the maximum acceleration of the hand-arm system.

The required values of the prototype consist of the mass $m_{p} = 518 g$ from Table 2, Young’s modulus for unidirectional fibres calculated by the rule of mixtures $E_{p} = 109 G Pa$ and damping coefficient $λ_{p} = 33.76 s^{- 1}$ obtained from the vibration analysis. The maximum acceleration occurs at $t = 10 m s$ after the impulse. This data is obtained from Figure 7, where the impulse is apparent at 40 ms and the maximum acceleration $a_{p, \max} \approx 150 m / s^{2}$ at 50 ms.

The required values of the X-Dream consist of the mass $m_{x} = 595 g$ from Table 2, Young’s modulus of aluminium 7075 T6 $E_{x} = 70 G Pa$ and damping coefficient $λ_{x} = 26.30 s^{- 1}$ calculated in the vibration analysis, with $t = 10 ms$ and $a_{x, \max} \approx 100 m / s^{2}$ from Figure 6.

Assuming that the spring constant is proportional to the Young’s modulus due to the identical geometry of the ice tools: $k \propto E$ and that the peak contact force F₀ may be considered approximately equal due to standardisation with the force plate, the ratio of the maximum accelerations is given by:

\begin{matrix} \frac{a_{p, \max}}{a_{x, \max}} = 1.50 \approx \frac{\frac{\sqrt{E_{p}}}{m_{p}^{3 / 2}} e^{- λ_{p} t}}{\frac{\sqrt{E_{x}}}{m_{x}^{3 / 2}} e^{- λ_{x} t}} \\ = \frac{\sqrt{E_{p}}}{\sqrt{E_{x}}} \cdot \frac{m_{x}^{3 / 2}}{m_{p}^{3 / 2}} \cdot \frac{e^{- λ_{p} t}}{e^{- λ_{x} t}} \\ = 1.25 \cdot 1.23 \cdot 0.93 = 1.43 \end{matrix}

(10)

This equation shows that the damping factor reduces the amplitude of the prototype by 7% after $10 m s$ , while the lower mass increases the amplitude by 23% and the higher stiffness increases the amplitude by 25% in relation to the X-Dream. At the second positive peak, $30 ms$ after the impulse, the enhanced damping properties of the prototype reduce the amplitude in total by 20% more compared to the damping properties of the aluminium shaft. The damping initially has a lesser effect than mass and Young’s modulus but gains influence over time. Consequently, the higher vibration exposure of the prototype and the Morpho is attributable to the higher maximum initial acceleration. However, the calculated factor of the model 1.43 only approximates the ratio of the maximum accelerations, which, based on the measured values, is 1.50.

These findings demonstrate that the prototype’s rubber interleaved composite shaft would reduce the vibration exposure under the assumption of identical mass and stiffness, in comparison to conventional ice tools.

Light weight versus high peak contact force

The lower weight of an ice tool offers ergonomic advantages, as swinging and holding the tool are fatiguing activities. Therefore, lightweight design is considered a key requirement, even though it inherently reduces the peak contact force – a parameter that should remain as high as possible. The results suggest that the mass distribution plays a role in the rebound and the shock impulse. For instance, the Morpho ( $395 g$ ) exhibits lower acceleration peaks than the prototype ( $518 g$ ) despite being lighter, presumably due to its centre of mass being closer to the head. Although the Morpho is lighter, it utilises its weight better because its handle is made of composite material. Whereas the handle of the prototype, although more ergonomic, is heavier and requires an additional mounting insert, adversely affecting the centre of mass.

Trade-offs between stiffness and damping

The presented model illustrates that increased stiffness leads to a higher vibration amplitude measured at the climber’s hand. In this context, the higher stiffness of carbon fibre is disadvantageous compared to the lower stiffness of aluminium. Stiffness can be reduced and tuned by interleaving rubber foils and aramid fibres. Consequently, incorporating rubber foils not only increases damping through internal friction but also has the potential to reduce the vibration peak amplitude of the hand-arm system due to reduced stiffness. Furthermore, fibre orientation can be adjusted. Studies have shown that fibre orientation influences damping behaviour; by trading off flexural stiffness, a substantial increase in damping ratios can be achieved.²³

Limitations

Prototype strength

The prototype was manufactured with a hand-layup vacuum pressing process, potentially leading to disregarded imperfections such as voids and suboptimal fibre alignment. Industrial manufacturing methods, such as autoclave curing, typically produce higher-quality laminates and are recommended for serial production.²⁴ Secondly, the material removal to accommodate the mounting inserts reduces the strength of the prototype but was necessary due to the uneven wall thickness of the shaft, which is attributed to the overlaps of the layers. To further optimise the fibre layup, more detailed finite element analysis is required.

Peak contact force standardisation

Standardising with smoothed peaks is not as precise as integrating the force over time and calculating the impulse. Local variations in ice properties, despite controlled preparation and storage, represent a confounding factor in on-ice impact testing. The estimated peak contact force values serve as qualitative standardisation metrics; the true physical peak forces are expected to be higher.

Impact vibration test

The hand’s anatomy as well as the individual striking and gripping technique affect the measured vibration amplitude. Additionally, grip force, exact hand position and impact angle can affect the measured vibration response, but were not quantified and only qualitatively standardised by the fixed setup and handle geometry. The study was limited to a single test subject; incorporating multiple subjects in future tests would enhance external reliability. It is recommended that in any future tests, the mass of the test objects be kept constant to eliminate this confounding factor so that the damping properties can be compared more effectively.

Furthermore, the use of a low-cost IMU represents a methodological limitation; future studies could employ calibrated high-quality sensors and a synchronised, high-bandwidth measurement setup to enable more precise measurements and allow FRF-based comparisons.

Damping oscillation model

For calculating the maximum acceleration, the characteristic values of the ice tools are used, with the real system consisting of the ice tool and the hand. The ice tool’s centre of gravity – which influences the impact impulse and the damping properties – is not considered. Thus, it substantially simplifies the actual tool-user interaction.

Conclusion

This study represents the first scientific research of the vibration exposure of the hand-arm system during the impact of an ice axe strike. Relative to the geometrically identical aluminium ice tool, the developed rubber-interleaved prototype exhibits a significant improvement in damping ratio. However, its lower mass required higher acceleration to reach the standardised peak contact force. The combination of reduced mass and increased stiffness led to a higher initial excitation, which outweighed the damping benefits during the first milliseconds of the impact pulse. Although the prototype’s overall improved damping properties are beneficial, they cannot fully offset the higher initial shock. The effects of weight, stiffness and damping on maximum acceleration response were illustrated using a mass-spring-damper model.

Still, the developed prototype shaft offers advantages over traditional composite materials regarding the enhanced fracture toughness provided by the embedded rubber foil and weight benefits over aluminium shafts due to the high tensile strength of the carbon fibres. Together with the increased damping capacity, these advantages make the presented prototype a promising innovation in ice tool design.

This study sets a solid foundation for the further development of novel hybrid ice climbing tools. Future research should optimise the trade-off between weight reduction, stiffness and vibration damping for better ergonomic results. The influence of handle geometry and mass distribution should be explored, as these factors can significantly affect impact behaviour and vibration measured at the climber’s hand.

In summary, while damping can mitigate vibration exposure, the results clearly show that mass and stiffness dominate the initial acceleration response. Balancing these parameters is therefore essential for achieving both high impact efficiency and reduced vibration transmission in ice tools.

Footnotes

Acknowledgements

The authors would like to thank Fabian Stöckel for his support with the Kistler force plate measurement system.

ORCID iDs

Gabriel Girardini

Veit Senner

Ethical considerations

The author, who participated as a test subject, is an experienced ice climber and can confirm that the strike forces were within a range similar to standard ice climbing. The study was conducted in accordance with the Declaration of Helsinki.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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